Taz went through a not-eating stage a few months ago and we tried changing his food. We changed it about 3 times and I was just worried about changing it SOOO much. Finally, we found a food he could eat and keep down. It is only available through a vet, but it is Purina Veterinary Diets z/d. This is a food for sensitive stomachs. But of course, what worked for my cat doesn't mean it will work for Amber.
Good luck and I hope she gets better soon.