Looks s like it might be seborrheaic (sp?) dermatitis with the allergen as the root cause. I had an English Bulldog that had the same thing. The vet has some specific shampoos that may help this or you can try a human dandruff shampoo, maybe alternating with the soothing oatmeal baths. Gold Bond medicated baby powder can also help soothe the skin and itching, while keeping it dry so yeast doesn't set in.
Good luck, it may be a lifelong struggle :(
Sounds like you are already doing all you can for your dog. Maybe another idea would be to try keeping inside the house more, for less exposure to allergens outside. Blessings - Blu