Question:
My westie, Tally, is much better now. She is thankfully back to her cheeky little self. But her back end was still very messy, so we bought some mild puppy shampoo and bathed her in lukewarm water for three minutes. She enjoyed it very much and we made sure she was warm and properly dry. She is now sleeping, and looks much cleaner. We only made the decision to bathe her after we talked to the man who owns her cousin, and he assured us that both of his westies were bathed regularly and were fine.
So it'll be a monthly occasion.
Lexie, my hamster, is also much better. The rash disappeared and her fur is almost re-grown. I think it was just stress, but it could have been helped by some special powder I bought.
So, thanks to everyone who gave me advice and if I have any further problems I'll know where to come.

Answer: