Originally Answered: Should I drop this class?
If that's really what happened, and it happened to me, I would play offense, not defense. I don't take any unfair BS like that sitting down. I'd go straight to the dean to explain the problem.
Then I'd make her life hell in a way that she can't do anything about without losing her career.
I'd get to class very early, to get the middle seat of the front row. I'd start the audio recording app on my iPod and wait for students to arrive. Then I would stare at her normally, with a neutral expression, for the whole class, in a way that would be perfectly innocent to everyone else in the room. Then I'd wait until digs her own hole. She'll probably go postal very soon, and it will be her own fault. A student has a right to attend class peacefully and innocently watch the professor. Whatever problem she has, it's her problem. If she can't deal with it in a professional manner at all times, then she has no business being in that career. If she controls herself, then I'd still drop before the deadline, but her treatment of a student in that manner deserves giving her the rope to hang her own career.