Hi! I am playing my first dnd session. My character is a Fighter that started with 10 Charisma and now has 11 Charisma. Through the story he made a deal with a hag, becoming a hexblood. Our DM offered me to increase one my stat by 2 and another by 1 after becoming a hexblood. Should I increase the CHA by 2 and multiclass into a Warlock or a Paladin? Or is it a bad idea?

Good or bad by which standard? For story purposes it could be pretty fun. But from a character optimization standpoint, it would probably not work too well. 

That depends. What do you hope to gain by Multiclassing?

Well, more story features, I think. But if this multiclasseng will just ruin the game, then it would be better to up the STR instead and stop on Fighter, without multiclassing.

Nah, it’s very, very unlikely that it could even remotely ruin your game. You might not be quite as optimized as you could be, but that won’t ruin anything. This edition is very forgiving when it comes to stuff like that.

Story-wise, it’s not an issue; mechanically it depends what you’re looking for; when it comes to multiclassing Fighter it’s more typical for someone to dip into Fighter for a level or two for the early features. Performance-wise it’s not a massive boost to dip into Warlock or Paladin here, and trying to make that a new main class at this point is a very uphill proposition considering how much ground you’d need to cover. Honestly, if you just want to add some flavor to your character from the deal, I’d recommend just talking something out with your DM over a dip. Maybe look at feats and see if there’s something you want to take with that level 6 ASI for Fighters that you can use as a product of the deal. Or go for the multiclass, it’s your call.

Wait, what’s your fighter subclass? Because if it’s Eldritch Knight then a 2 level dip into Paladin is a fantastic proposition.

Oh, true.

Yes, it is a Human Eldritch Knight Fighter.

Then 2 levels of Paladin will make you love your life. In the long run you’ll break even on your total spellcasting potential, but you will sacrifice being able to learn 4th-level spells. But that’s not the end of the world because what you’ll gain in exchange is well worth it IMO. And rarely do campaigns hit 20th level, so you probably won’t even get a chance to miss the 4th attack per turn by not hitting 20th level as a fighter. In exchange you get 10 points of Lay on Hands to either supplement your Second Wind or pick up teammates with, a nice little ribbon in Divine Sense, and then the impressive stuff kicks in when you snag that second Paladin level because you’ll gain:

• Access to a whole suite of 1st-level Pally spells which are often way more useful than half the EK’s list, and most of them don’t give a damn how low your spellcasting ability is so only having Cha 13 won’t matter.
• Access to Divine Smite which gives you something offensively useful to do with your spell slots since all the Evocation options aren’t worth using after 5th level.
• A second Fighting Style.

Very worth it IMO.

Narratively speaking it's great, as others have said.  Fighter level 5 is a huge power spike.  What you do at 6 isn't a huge deal.  All you get is an ability score improvement for fighter 6.  A dip in warlock or paladin can be great.  You get a lot out of 1 level in warlock.  A few levels in paladin can be great.  But level 7 in eldritch knight fighter gets your second level spells which can be great.

It also depends on how high you go in your campaign.  If you're capping out at 8-10 then yeah multi class your brains out.  If you think you'll hit level 11, sticking with fighter will be huge.  Honestly, from a mechanics standpoint there are trade offs but both are going to be fine. Whatever you think makes the better story is the best choice.

To answer the general question posed - viability of multiclassing at any point is dependent on the DM style. I tend to tune encounters to party level, so unless you're being daft (Eg refusing to fight back or you just cripple your character, which would take quite some doing), then you'd be fine in my campaigns. At worst, you'd just take less attention from monsters. 

On the other hand, some DMs have either the attitude that you should adapt to their world, and if your character sucks then that's your problem, or they think it's their job to kill you. With the former, it depends on the party to carry you, with the latter...well, I wouldn't play with them, but some enjoy that...and your character has to be at the top of their game.

It depends on the DM's style, really. Plus how good the MC is, of course - some are amazing. Most, less so.