Are there any resources out there where I can input a specific magical item, and see if its obtainable in any campaign or other such module??

 If I understand correctly, you simply want the magic item database here.  Follow the menu for Game Rules.  If you search for the item in question and don't already own the module/source book it comes from, it will tell you which one it is and suggest you purchase it.

If you already own it here on DNDBeyond, it will list the primary source in the lower right corner of the item description.

On a magic item's description page, its in the lower right, just above the comments.

I don't know of any resources outside of here on DnDBeyond. You can find them here, but it takes some digging in the general search area. Looking at the item gives the first book they were published in, but in the search it gives you each instance it appears in. For example, you have to dig a little to find out a vorpal sword is obtainable in Lost Laboratory of Kwalish, or that a +1 rapier is in Forge of Fury and Acquisitions Incorporated.

Also keep in mind that there are official adventures where treasure/rewards earned have no items listed, and instead advise the DM to roll for them or choose outright. In these instances a specific item could be inserted that wouldn't appear in any resource. 

Quote from Sigvard_Vigrid >>

I don't know of any resources outside of here on DnDBeyond. You can find them here, but it takes some digging in the general search area. Looking at the item gives the first book they were published in, but in the search it gives you each instance it appears in. For example, you have to dig a little to find out a vorpal sword is obtainable in Lost Laboratory of Kwalish, or that a +1 rapier is in Forge of Fury and Acquisitions Incorporated.

Also keep in mind that there are official adventures where treasure/rewards earned have no items listed, and instead advise the DM to roll for them or choose outright. In these instances a specific item could be inserted that wouldn't appear in any resource. 

 Yes I came across 1 or 2 mods where it left it up to the DM's discretion as to the choice of magic item (Either rolled or random). So if I were to play one of those and the DM were to be generous and award me say a efficient quiver, for my ranger, how would I be able to use it in other mods if a different DM were to question how I got it? 

Are you talking about Adventurer's League (AL) or just home games / non-AL games at a gaming store?

Quote from Houligan >>

Are you talking about Adventurer's League (AL) or just home games / non-AL games at a gaming store?

 AL sanctioned play

If a magic item is found during an adventure it is "unlocked" for all players in that adventure. If you are under the magic item limit for your tier, you may keep it and add it to your logsheet.

Quote from Houligan >>

If a magic item is found during an adventure it is "unlocked" for all players in that adventure. If you are under the magic item limit for your tier, you may keep it and add it to your logsheet

 I was under the impression that I could own any number of magic items that were found while adventuring, but was only allowed to "Equip" (Per adventure) 1 for Tier 1, 3 for Tier 2, 5 for Tier 3 and not sure what the Tier 4 limit was.

From the FAQ (free, in the Players and DM Pack on Dungeon Master's Guild):

Except as otherwise specified, all permanent magic items that your character possesses counts towards their Magic Item Limit except items of common rarity and story items.