Since Bella Swan was on my team and I went with Snarky Bella for various reasons, I don't have to worry too much about certain real world concerns. But for those who don't have someone with a time machine that's bigger on the inside on their team, real world concerns matter.
You see I have disabilities. There's a reason, for example, that depression gets its own index. So if I had those three I couldn't be assured of getting the medical supplies I'm getting now, and if I did it would involve breaking into and looting pharmacies and such.
More likely I would have to explain that I'm going to become more and more useless as the antidepressants work their way out of my system. If we are breaking into pharmacies and such then those are otherwise unnecessary and potentially risky excursions, if we aren't then I have to take into account that for the majority of the time I'm going to be under the influence of untreated depression.
Protagonists are protagonists. There are probably all kinds of things that can mess things up for them, but they're still protagonists.
You are you. If you have a disability then you've got to consider how having a person with that disability, you, on the team is going to affect things. If you have phobias or neuroses, if you have anything that differentiates you from "generic person" be it good or bad (and I'm betting you do) that's going to have an effect upon the team.
It may be that the most interesting part of your zombie apocalypse team isn't how the three protagonists work together (or fail to) but how they work together with you. You're the fourth member of the team, and that means that your team will be different than someone else's even if they have the same three protagonists as the other members.
Maybe you're helpful, maybe the need to look after you and keep you alive slows them down considerably, maybe both at once.
Previous things written on the subject of zombie apocalypse teams:
How to make your Zombie Apocalypse Team - Explains in general the considerations one must make, borrowing/stealing heavily from "Part Alpha" below but in a more general way because this is about how you make your team rather than how I make mine.
My Zombie Apocalypse Team:
Part 3 hasn't been written yet
[unknown unwritten parts]
[recruiting the remaining two characters]
[More unwritten stuff]
[More unwritten stuff up to the end.]
 Die Hard. I know I linked to a set, but I'm thinking the original. If you haven't seen it in recent years then the first time you watch it your reaction will probably be, "Oh my God! He has hair."