I had a dog with skin problems too. She would scratch and chew and itch till she was raw. But she never got scabs like yours. Vet told us to switch to a grain free dog food because that's what allergies in dogs usually are (didn't even give us the option of testing, we've since switched vets) Tried many different types of prescription dog foods, one even looked like Kix Cereal
Finally found Taste of the Wild food at my local Tractor Supply store and it was cheaper and faster to get it there than going through the vet for prescription dog food.
However, nothing seemed to help. So we finally got her tested and turns out that grains weren't the problem at all. It was mostly meats, beef, poultry, fish, venison, the list goes on. You know how hard it is to find a dog food that doesn't have beef or chicken in it? Very. But thankfully, Taste of the Wild had a Lamb variety that would work and it meant we wouldn't have to switch dog food brands again, just flavors.
Well, that still didn't help. So we started giving her allergy shots. Still nothing.
We came to the conclusion that it was a yeast infection of the skin, though it was never professionally diagnosed. She smelled gross and bathing her with an anti fungal shampoo helped but only for a few days. And sulfur and lard on her wounds helped too.
We never found out what was truly wrong with her. We lost her due to an unrelated problem.
Keep a very close eye on her, watch (or even document) what she eats and see if it causes flair ups. Good luck and I hope she feels better. It's no fun being itchy.