Obviously your dog may have environmental allergies. Intradermal skin testing is the only accurate way to identify the allergens. I can’t believe your veterinary dermatologist hasn’t recommended this?
Then you can identify the treatment options. Allergen specific immunotherapy (desensitization) subq or shots is the most natural treatment.
There is no cure. Atopic dermatitis is a serious condition and requires lifelong treatment. It has nothing to do with the food.
The skin discoloration you describe is hyperpigmentation, common in dogs with environmental allergies.
There is no cheap way out of this, testing will run. close to $1000, maintenance will run a few hundred a year.
There are no miracle cures for this condition.
Use the search engine to see my posts, /forums/search/environmental+allergies/
Good luck
