I am trying to build a 5e Female Adult Silver Dragon, "Andrea Mavis Glori" (I am a Silver Dragon) posing as a young female human to put into the campaign that can lend her aid to my 3 party adventurers for tougher fights. She would be in the background, and help with role playing, and used to sort of railroad/hook if the players are getting more off track than I am comfortable with. I am trying to keep true to dragons for the most part, but not completely. And I am trying to make it seem like, once they realize she's a dragon, that they facepalm for not noticing it sooner.
So far, I've got the name, Andrea Mavis Glori. I'm considering using a 16th level sorcerer, only cold/ice spells, illusion spells, and a few others that match the dragon flavor (I.E. Water Breathing, Levitate, Control winds). I have given some very powerful magic items/flavor items-Dragon Scale Mail (Silver), Staff of Frost, Wand of Paralysis (which I think I will build into the staff), Goggles of Night and Ring of Mind Shielding. abilities are S/10 D/14 C/10 I/16 W/13 Ch/21

Initially I wanted sorcerer, since she has such a high charisma, but now I just want a class for flavor, since she is just going to be helping, and doesn't need to be overpowered. I figured a CR 16 in dragon form should equate to a level 16 in human form. I did not keep the HP as suggested by the DM guide, since it didn't make sense without maintaining the size or constitution.

So my questions are, 1. Is sorcerer the right class for this? Or might there be something better? 2. Are there more magical (ideally canon/non-homebrew) items that would be fitting of a silver dragon?

https://ddb.ac/characters/8849954/sYtCnO (Work in Progress)

I would say: don't do it at all.

If you're having trouble with your players getting distracted or going "off the rails" your group should have a long talk.  They might want something, as players, that you're not providing as their DM.  Adding an ultra-powerful GMPC usually just ends in the party not having fun, especially when they're forcing the plot.  Using a ultra-powerful GMPC to railroad the party, in my experience, never ends well.  Your players should want to follow your plot.  If they don't, listen to what they do want to do, and do that instead.  Running games your players want to play in is the path to success.

Find out what your players want, take notes, then give it to them.

Thanks for the advice, but I'm really looking for advice on how to build the npc. Not how to implement (or not to implement) her into my story.

But since you mentioned it; I'm not planning on railroading my players, more like using her as an indicator that they are on the right trail for a specific quest line. Using her as a hook more than a forcing move. My players will always have the ability to follow her or not, and will only encounter her on the main story line. Ultimately she may turn on them, or they may end up helping her. I plan on building her as one of many NPC hooks. Having politics of dragons in human forms, creating bonds with the players that will create conflict as they have to choose between one npc they've grown to like and another.
What I meant by "railroad/hook if the players are getting more off track than I am comfortable with" is if i can see they are getting frustrated, and I don't want to simply give them they answer out of character. It's nice to say "they should want to follow your story" but sometimes they do something unexpected, and it's nice to have an emergency cord built into the story line. Sort of like an escape room where they build in hints, just incase.
I got the idea after another campaign I had took a weird turn as my players basically turned into the bad guys just because an NPC they grew to like that was adventuring with them turned out to be a bad-guy himself.
I chose a Silver Dragon, because they can be extremely versatile with the items and relics that can be found in their hoard, and their gregarious nature is easily liked.

So with that said, any advice on how to class and equip a dragon posing as a human?

The class would work just fine, however the question that you might want to go with is: what role are they missing that she can fill?

Second: she's a dragon, why are you giving her PC stats? Just fluff the information, jot down the spell list and make the rest of it happen because it needs to.

Third: If you truly are going to make her an NPC then don't let her stick around for very long when she does show up.

I have an Ancient Gold Dragon (Ari) that shows up at random times. He showed up with a group of Halfling NPCs and talked with the PCs for a while, it was a perfect opportunity to give them all more history about the world, information that was important to the current plot, start up a couple character story arcs, and just create a fun RP scenario (they didn't know he was a dragon at this time).

The next time they met him, he was just wandering around the country side and happened across them. He joined them as he was curious about their destination; Iron Haven. During the journey he helped them fight a very high leveled spell caster (he broke down a wall of force), he helped bandage a handful of Elves with the aid of the group's Bard, and "accidentally" used too much energy to close a planar rift (this is where they started to guess he was a dragon).

The last time they saw him they were just finishing up a fight with an Earth Elemental, a Kord, and 3 Basilisks, the group was in bad shape. He cast Mordenkeinen's Mansion and invited them in. While in the sanctity of this spell he revealed himself and explained a number of things that the group had questions about. He also explained why certain events were happening, simply a way that I (as DM) could give them relevant information in an RP manner. As well he broke the Barbarian's arm in an arm wrestling match on accident...

But through all of it Ari was of little help except to take care of things that the players had no chance of dealing with on their own. He was a tool to help push things along rather than save the players from themselves and their actions. It's fine to have these types of NPCs, but they need to be brief blips on the screen, it will make them feel special, give you the chance to build into the "face-palm" moment, and still let the players keep the spotlight on themselves.

@DMThac0, sometimes I will let the players control the NPCs, it makes it easier to allow them to strategize without my input and connect with the NPC. and giving player stats gives them exposure to other classes, without needing to roll a character.

I agree with DMThac0 regarding what holes are in your current group. Also, I'm curious as to the level of your party. Because if they're down around 3/4ish, throwing in a level 16 anything is going to be so OP it may ruin their fun and just make them feel rather useless. If that's the case, tone down your dragon into a wyrmling or something. Also, don't get too caught up with the dragons stats changing when they shape change. They're still a dragon, so HP and Con shouldn't change. It also gives you the option of using them as a shield in certain situations that maybe should TPK your guys, but the dragon could throw herself into the gap and take the full brunt of the onslaught (leaving her weakened, but maybe exhausting that high level spell slot of the BBEG that makes it achievable for the party to take them down).

Another thing to throw in there, both as features of the NPC and also flavour, are immunities and resistances. She doesn't feel the cold. No matter how cold it gets. Another one of those bits that the PC's SHOULD put together, and adds to your facepalm moment that you're after. Also historical objects. Silver's love history. So items they have on them would *probably have some sort of historical significance, which the dragon would enjoy talking about. Something I've done in my games is give handouts, excerpts from various books about history or wildlife that a player has learnt through either study or conversation, and give that player a +1 on checks relating to that. So the dragon might want to talk about history, and if the players are willing to engage, then they might spend a night around the campfire hearing tales of some city, or a time period, or whatever you want, and then they get a +1 for checks against that info. But you just give the handout and they can read it at their leisure, cause no one wants to sit there while you read a whole chapter of the Book of Nine Hells.

@MajorPuddles Yeah, that was exactly what I was thinking in terms of history, lore, and storytelling. 
Also, PC lvl's will be around 12 when this NPC joins them in any fights, so if they decide to murderhobo her, they will actually stand a chance of surviving her defense, or even beat her if she reverts to a dragon form.
I can tone it down into a wyrmling, but I feel that it will just create plot holes for the reveal... like why is such a young dragon so knowledgeable and traveled (almost the same problem with a young dragon, and not as epic a reveal).

As far as the change shape, I was referring to the skill as it reads in the monster manual.

In the change shape form, only the mental traits (int, wis, cha) are maintained, not the physical (str, dex, con). I decided that the HP would also be more that of a human, since it is a physical trait, and I can build in a mechanic that once she reaches 0hp in human form, she can revert into her dragon form after failing death saving throws, instead of dying (or something to that effect). I didn't really make sense to me that a dragon could change shape into a cat with 243 hp and 18d12 hit die. Also why I like the staff of frost and dragonscale armor, it is explained by the "change shape" ability, and had a certain flavor to it.

I know I can fudge stats, but I want it to be subtly obvious, not glaringly obvious... like "why does this sorcerer have more hit points than our barbarian" if they ever control her/see her stat sheet.

If you are handing them the NPC to control in combqt, then just hand them a fairly regular lvl 10-14 storm sorcerer. Justify it to yourself that this is the level of power the dragon is willing to use to aid them. When the NPC is in your control then it can exhibit other traits. Even hide certain powerful artifacts it is carrying that you could use but the party need not see. If it "dies" in combat then have it disappear by some magic and come back later with yet more suspicious dragonny clues. 

@regentcorreon excellent idea! I love it. Continuing with your thought, just because they are controlling her, it doesn’t mean they need to have perfect knowledge of her.

also, storm sorcerer is exactly what I was going for without knowing it. Definitely gives me more direction. Thank you.

This might help anyone looking into this in the future, but this thread is surely being necro'd by me (oops).

You mention "I didn't really make sense to me that a dragon could change shape into a cat with 243 hp and 18d12 hit die." but it's important to note the ability: Change Shape.
The dragon is assuming a different form, but they retain "hit points, Hit Dice, ability to speak, proficiencies, Legendary Resistance, lair actions."
That cat that got kicked and didn't die? Unusual and cryptic, a mystery to solve, or maybe an obvious shape changer. It doesn't necessarily reveal the cat is a Dragon specifically, but it does lead you to believe that creature has something else going on that could be worth investigating.

The reason it maintains its hitpoints is because it is NOT Polymorph. Change Shape does not add a pool of hitpoints; if the Dragon reaches 0HP in their different shape, their form reverts into a dead dragon.
The feature also specifies the Dragon will not get class levels or features. However, you can give them innate spellcasting (could include spell slots or x/day) that the dragon can maintain between forms. To be convincing, the Dragon might assume the appearance of a long-living race (elves are very likely) and wear equipment that makes them appear of a 'class' that has the same spellcasting capabilities. Red dragons might choose sorcerer garb, blue might choose wizards, green could be a politician or bard.

Magic items are assumed into the form when it changes shape, so maybe have human equipment and dragon equipment. For example, Ioun stones can be used by either form, so they could be borne by both forms, but a staff of lightning might only work for the humanoid form depending on how you want to rule it.

Well, I'm a very new DM and not someone you should probably ask but since its a dragon maybe just lean into her personality and think about what her class could add to her personality/theme; as in she could tell stories like a bard or be skilled as a guide and in nature (or at least that's the feel I get from a ranger). She is a dragon, so if you want her as a protector sort of NPC or a consultant (in my mind) you don't have to add a class.