I would have a word with her form tutor and see if her behaviour in this lesson could be monitored (we use monitoring sheets to do this where I work).
I can see that it is tempting to hoik her out, however she would be better sorting out some coping stratgies, much more useful in the ong ter.
Re the 'He is picking on me' thing. I'll confess that there are kids who think that I pick on them. I don't, I pick on their behaviour. I asked a whole class to assess my teaching, one of the questions was Is your teacher fair, does she pick on you?
Two kids out of 26 said yes.....you guessed it the disruptive ones
The teacher should get the name right, however we are only human and there are ways and ways of correcting the teacher!
Contact the form tutor and have a chat. Ask him/her what could be done. If it were me I'd suggest a monitoring sheet and some soft rewards if she does well, from you, and also praise from the teacher.
HTH. Changing teachers will just duck the central issue, which may well persist as she gets older and the hormone pixie comes to play