I agree go for a second or even third opinion. Our ET was taken to a very high priced vet that we had used for over 30 years, but something didn't seem right. I took her to another that was highly recommended. After 3 visits and two different vets at the new clinic. She passed and we found out it was cancer. I at lest know that I tried.
We have had hair loss and it almost always comes back to diet. Good luck and please let us know how she does.