It kind of sounds like maybe the begining of a staph infection, but if so your dog will start to loose it's hair in those spots & yes only antibiotics will work. (My dog once had staph while visiting Arkansas and his patches were about the size of a silver dollar some bigger although his skin was not too red mostly ghostly white w/ some reddness on the outskirts & really flakey of course he has very very thick fur so it was hard to tell at first but he was on antibiotics only a week & a half it cleared up great)

I doubt it is ringworm they look more like really bad black fly bits, almost like a black & blue mark and it is very contagious to all animals & humans.

Most likely it is an allergy to something or other. You say this is the first time they have looked like this? If so has anything changed recently? Like her food, any cleaners used around the house, etc?

By giving her a bath so often may actually be causing it to get worse. I would suggest a vet appointment & allergy tests, they are not to awful expensive & they will save a lot of money, time & trouble for both you & your dog in the long run!