I think I'm overreacting towards a student
Why are you overreacting?
She annoyed me when she looked at my girlfriend
People have the right to look at anyone or anything that they want to. You are trying to control other people and limit what they can do and that is not realistic.
I just found her staring at my girl friend annoying.
Even if that's the case, you can't control who she looks at. Be confident in your relationship with your girlfriend.