Please help me! Rat tail skin fell off?

I was holding one of my female rats by her tail to give her a bath. She spun around, then about an inch of skin on her tail fell off and she dropped into the bath. Her tail looks like a white string, and it was bleeding every where. I put her in a separate cage (I have two five foot cages, six boys and eleven girls.Pet shop owner accidentally said two girls two boys, it was actually three boys and one girl...) And she kept crying her little rat cry, and trying to eat her tail off. It looked horribly painful, and every time she moved she screamed. I know lizard's tails fall off if they feel threatened, but is this normal with a rat? She has completely stopped eating and drinks a lot. I put band-aids and neosporene on the tip of her tail and i am observing her every day. (it has been 2 days). When i put her back in the cage she wouldn't even eat with her sisters. :( I am very worried about my rat. Right now she is sitting on my shoulder asleep, but everytime you go near her, she cries and licks you, like crazy. PLEASE HELP ME. I would bring her to a vet, but they do not deal with small rodents. :'( Should i cut off her tail completely? (Evil dad suggests this.) Should i keep her under more watch, or put her back in the cage with the other females? (they try to bite her tail too.)