I don't see why she shouldn't get angry back, thats a natural thing to feel and because it is natural I can't see it just going away. Whats important is how she responds to it so first let her know the feeling is ok its the response that needs work.
Maybe some role play would help, you pretend to be the person winding her up and listen to her responses and vice versa but this time you respond assertively and positively so she can see how she can express herself without leaving her feeling bad about it. Use situations that have actually happened to show her what might have happened had she had more control over her feelings. In school give her a code she can say to a teacher that means I'm getting wound up! without actually having to say those words, maybe she could put her hand up and wave it or something, and then the teacher can support her with it too before it gets out of hand.
Could be hormones acting up too, they can start impacting on a girl around her age, maybe a trip to the doctors for some advice?