Your options sorted by how much DM approval they need, sorted from least to most:
Rules As Written: Warlock
RAW, the only way for you to get yourself a pixie companion is to be a level 3 warlock and select Pact of the Chain specialization. (Technically it's a sprite and not a pixie but I assume "flying tiny fairy" is what you're looking for). So you could multiclass into warlock. You'd pick up some useful spells (Hex in particular) and your sprite would be more effective than a normal familiar, but it's not an optimal choice and you wouldn't get your pixie for 3 more levels.
Refluff Familiar: Eldritch Knight or a Feat
With the level 1 spell Find Familiar, you can get yourself a fey animal as a familiar. A sprite, like the other alternative familiars, has features beyond a normal familiar and is not in your list of options for the Find Familiar spell.
However, flying is an option (a hawk or owl), so fairy without extra features wouldn't be unbalancing. If you talk to your DM, they might be willing you to refluff (meaning change the description of a spell, ability, class, etc. without actually changing the mechanics.) your familiar into a tiny winged person instead of an animal.
In which case, getting the Find Familiar spell is much easier. At level 3, you can choose to become and Eldritch Knight, gaining 3 level 1 wizard spells, one of which could be Find Familiar.
If you'd rather not be an Eldritch Knight or you don't want to wait until level 3, you could use your variant Human feat to pick up Magic Initiate. It gives you two cantrips and one level 1 spell. So for the cost of a feat, you've got a familiar from the beginning and you're still free to pick whatever fighter specialization you want.
Background: Noble: Knight
I think most DMs would be willing to let you refluff your familiar as long as you aren't expecting any extra mechanical benefits. But what if your DM is feeling generous?
The noble background has a variant (Knight) that allows you to have three retainers. They are explicitly commoners who will only perform mundane tasks and not participate in combat at all. But it doesn't specify their race. A generous DM might rule that one could be a pixie.
Roleplay It
Finally, you could find an NPC pixie. All previous points have focused on mechanical character features. They assume that you're trying to have a companion under your direct control. But Navi wasn't a class feature. She was a quest feature.
If you can convince a pixie that your quest is worthy, that you're just so awesome to hang around with, or that you will reward them, they might follow you around. This could happen in game, or you could discuss it with your DM as part of character creation. Work together to come up with a backstory that explains why a fairy wants to follow you around.
Just be prepared for it not to necessarily be an entirely beneficial situation. Maybe the pixie isn't actually following you out of benevolence, maybe you wrecked their grove and won't leave you alone until you make amends. Maybe they'd be lacking in social graces or will give away your position. Or maybe they'd be really annoying.
Unlike some previous editions in which the fireball will adjust based on the space available and spread down corridors if contained, 5th ed simply states that the fireball will take up the amount of space listed as 20' radius sphere and spread around corners to fill that space, never expanding to exceed that distance from the point of origin. This specifically breaks the line of sight rule on page 204.
So if cast at the entrance of a 10x10 room with a 5' corridor leading into it, it shall fill that room and spread 20' down the corridor.
Fireball PHB PG 242
The fire spreads around corners.
Best Answer
Magic is unaffected by creature size. Creatures can have benefits for particular types of magic (it’s easy to imagine a dragon getting bonuses on fireball—after all, their descendants do—or a pixie getting some benefit with illusions), but nothing automatic just for being larger. Any such benefit would be listed directly in the creature entry.
For reference, this is also consistent with previous editions of Dungeons & Dragons. The premise, presumably, is that magic cannot be judged on physical grounds, and it’s in magic’s very nature to surprise you.