almost seems like one of those diagnosis of "it's not in this category". In another words very non-specific.

If this was your regular Vet that made the diagnosis, you should consider getting a referral to a doggy dermatologist. It might be just as likely that you are dealing with an allergy, thyroid or misc metabolic condition, mange, or another skin problem. The point being the more you can define the problem the more likely you can find a more specific treatment.

Definitely keep the dog on the antibiotics to prevent skin infections while trying to get a more detailed diagnosis. You might also try supplementing the diet with fish oil and Vitamin-E. Both have been shown to help the skin recover from damage due to various skin problems.