The half life amoxcillin is pretty short. Honestly, it would be way way out of her system after a week from her final dose. I'd say that the vomiting isn't related. Rash is a side effect of pen. antibiotics but am wondering if perhaps she has picked up another virus????
I'd call the doc to check out a rash lasting a week after amox. usage. good luck
another thought make sure she is drinking plenty of water and using the bathroom so she is not dehydrated.good luck let us know how she is doing.
It does sound as if she is still having a reaction to the amoxicillin including the vomiting, it may be best and for peace of mind to speak to your pediatrician again, I am assuming that you discontinued the med.