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I would go with a limited ingredient diet or raw and give benedryl(1mg per dogs #) and stay away from the steroids! Humidity in the house helps as well. Dry air adds to the dry skin.
Also natural vitamin C is a natural anti-histamine/anti-inflammatory...start at 500mg and over a week or two up it to 2000(split the dosage between mealtime) Quite possibly, your dog has environmental allergies which can only be pinpointed thru lab tests. There is a new way to give anti-serum orally so injections aren't an issue. Ask your vet or find an allergist to help you. It is costly to have the tests run, but once you actually find out the cause, you can have this managed. I've read where seacure is very helpful in managing the problem.
I hate allergies!
Canine Allergies and Your Dog's Health - Whole Dog Journal Article