Pitbull is itchy.

I have a 4 year old pitbull/lab mix that has been scratching and biting at herself. She bites and scratches so hard that she has lost most of the hair on her sides and her back legs. Sometimes she even scratches to the point where she bleeds. Her hair has gotten extremely oily, yet it seems like her skin is flaky. We had her to the vet twice and I believe all they gave her were antibiotics. The first set of pills seemed to help her, but then when she went off of them the problem developed again. We assumed she just needed more medication so we took her back and I think they gave her the same pills again. This time the scratching did not stop and she did not seem to grow any of her hair back. Ive tried to switch her food, but it didn't help. Im not sure if there maybe is a certain brand of food that will help her the best or not. Currently we have been putting salmon oil in the food she is on now which is purina one. We started that a few days ago, but she just keeps biting. I don't know if the salmon oil is enough to be giving her. Often she will lick at her paws too. Ive had to take her collar off of her because it seems to irritate her neck or will cause her to lose the hair on the front of her neck. Red spots also appear on her chest and underneath her and sometimes look scabby. After she gets a bath it seems the next day the oily hair and dry skin is back. Any help will be very much appreciated!! Thanks!!!!