From what you describe, it sounds environmental. Food allergies are rare. Food sensitivities tend to result in GI disturbances such as vomiting and diarrhea. Environmental allergies tend to show up as pruritus, ear infections and such.
You could try a limited ingredient grain free food. My dog does well on Nutrisca Salmon and Chickpea. Wipe down her feet with water and gently dry when she comes in from outdoors.
Bathe her using a gentle shampoo, I use Malaseb (see chewy dot com).
I tried all kinds of things times 1 year (including going back and forth to the veterinarian), but, did not get results till I took her to a dermatologist for testing. Allergen specific immunotherapy worked in her case.
