Conversations like that between closer friends shouldn't be much of a conflict.
Well, I think it's a weird anxiety thing. I haven't actually talked to a doctor or anything about it, but it crops up a lot, so I should. I know it probably won't be a big deal to talk it out, and she'll probably even apologize, she's not a bad person or anything. But the potential is there and that's what I fear. I know it's irrational.
Well, it sounds like you're either:
a) Afraid of losing the friendship, which in itself is normal and commendable, but if you take it too far you ran into the risk of falling victim to abusive interpersonal relationships - if someone makes you feel like shit, they either do it unwittingly, in which case you should tell her that it makes you feel bad for the benefit of both of you, or knowingly, in which case they are the ones who should take steps to make sure YOU are the one interested in continuing the friendship, although you stated this is not the case; or
b) Afraid of conflict itself, which suggests that you think, consciously or not, that you're going to lose - which means you don't think your case is good enough. Well, it is. Emotional abuse, intentional or not, ain't a thing anyone should be free to dish out.
Also, she seems really, really neurotic. Or she cares far less about the friendship than you.