While it is nerve wracking, Screaming won't hurt her. My son was (and sometimes still is) going through a similar thing. When he starts to throw his fits, I ignore it, if he gets louder, or more rude about it, I hold him on my lap, facing away from me. Just hold him there (not roughly, but enough that he can't get down or turn around), for about 2 minutes. Usually, it stops at about theone minute mark, but other times it takes the full 2. My Ped had Reccommended this technique to me right after his first birthday (he's 18 months now), when the fits started up... but I didn't give it a try until last month. It's effectively like a time out for kids too small to be in a chair or for kids who won't stay in the chair no matter what you do.
My son isn't broken of the fits yet, but they are no where near as bad, loud, or screechy now, and tend to stop a lot faster.
Good luck!