A few thoughts. The first is Ring Worm- but your vet should be able to recognize that. You can treat it topically with Ivermectin applied on as you would any other ointment.
The other allergies, either injested any feed stuff[hay/grass/feed/supplements...] anything that goes in her mouth. Or topical, new bedding, no bedding,fly spray different shampoo.
Not seeing her can't say for sure.
But similar, got a very skinny pony from auction, had a beautiful haircoat[although dull] Brought him along slowly with hay first,wormed him. Spring starts grass comes in starts {shedding?} Try to help it along by brushing-all hair comes out. NAKED
Is allergic to proteins- can ,maintain on whole oats and over the counter antihistimines.
Did your vet do a skin scrape when he shaved/cleaned the area. Would probably have @ least that done.