OK, if you were trying to avoid her, why do you care, that she's avoiding you back?
Also, who the hell ever said apologizing was unmanly? You people take this shyt too literally. You acted like a child, and you're asking whether you should apologize or not? YES, apologize. Avoiding chicks is AFC, btw. The alpha thing to do, is get in their space, and drive them away, if you dont want them around.
And, to clue you in, about the apology thing: the rule of thumb is, keep apologies to a minimum, and only if they're warranted. The point is, dont give up your manliness, by apologizing whenever she's pissed for no reason, aka, being a woman. And dont ever apologize unless you knowingly did something wrong, which you did.
Example:
Last night, I was at the bar, and this chick who led me on once was there. I am cool with her, but I like to fvck with her at the same time. I grabbed here boob, and she got mad, so next time I saw here I grabbed her ass instead and was like "hey, you just said dont grab your boobs" (so everybody knows, I was not doing this in a creepy way)
Anyway, the new bouncer at the bar comes up to me later and says "dont ever grab my girl." I was like "Who is that?" and he told me it was her. I said " I didnt know she was anyones girl" and we shook hands, but I was trying to be all alpha, and condescending towards him, cuz I know this chick pretty good, and she's a little slvt anyway.
Then I thought about it, and realized that I disrespected him, so a little while later I went up and introduced myself, and told him that I didnt mean to disrespect him, and it wont happen again, and I thought she was single, and shook his hand for real. However, I didnt apologize, because I didnt know she was anyones 'girl', so I didnt KNOWINGLY do anything wrong. What I did, was own up to the fact that I disrespected him, and told him I wouldn't do it again.
Also, I sure as hell didnt apologize to her for grabbing her boobs. I only did it cuz she comes up and grabs my nipples sometimes, so thats fair game, in my book. I simply told her that she deserves it for wearing a shirt with rhinestones on her tits, and commented about how girls always flaunt their tits, but get pissed when guys look at them, and how stupid they are. This chick is cool, but she pisses me off, so I always try to make out with her, just to see if she'll do it. I think she thinks I like her, so its funny. She led me on when i first met her. I didnt know or care who she was, then she made the moves on me, and eventually, I reciprocated, and she backed off and ljbf'd me, and even though it means that I did something wrong, I hate chicks that do that, so I fvck with her a little, and am kind of a dyck, whenever I see her (but not TOO much). The thing is, she puts up with it, and likes me anyway, and buys me beers and stuff.
Does this make sense?
EDIT: and one more thing. Her anger towards you is a sign of emotion, which is always a good thing. I've turned chicks hating me into lays, on several occasions. Be an a$$hole until they call you out on it, then apologize, and be nice to them. It stirs their emotions up, and creates a lot of attraction. Like your other thread, hatred is not the opposite of love. Essentially, they are very similar emotions. You know how in movies, when the main characters hate each others guts, then all of a sudden they start making out, and fvck? That works in real life. Capitalize on it.
Chicks need their emotions stirred up!
If I were you, I'd make good with this chick right now, and, make a move immediately, while her emotions are still running hot.