When that happened to me the prof did take me on unwillingly as a teachers pet. A couple of female students got bitchy every time he chose to put my writing on the overhead and not theirs. He did this all the time and it annoyed me too.....Then they got to let it out in the Q and A sessions......
Well why did you do this? Why did you say that? Bitch and moan bitch and moan.....If you don't really care they can't box you in a corner. I still don't care. I'm not around to solve other peoples psychological issues. Even then I was too old to take it on....When they rose their hand I got to answer their stupid question straight-faced. And they always came out looking even more stupid because the answers that came out of me definitely sounded obvious....I bet the girl is going to end up ridiculously stupid if she survives.
You are probably hotter and skinnier than her anyway, and have more experience. Ignore the jealous lil bitches of the world..They are always the ones with the loudest mouths. And if she really starts to annoy you- pop her ever so slightly on the mouth outside of class. I mean she has to expect you to have a bad day at some time......