She may have dry skin. How big is she? - if she is small to medium size, put one 1000 mg fish oil capsule in her food each day. If a large dog do this twice a day.
I have a rescued airedale. His coat was like wire when we got him and he scratched. Now he doesn't scratch and his coat is very soft.
The fish oil is good for her heart too. We have given this to our dog for years now.
Meanwhile til you get it under control, maybe you can ask the vet if you can give her something like Benadryl. Poor dog must be uncomfortable.