Welcome to EBN!
He may not have a food allergy but it could be environment or maybe his eye lashes.... Have you had the vet check to make sure his lashes are nit growing wrong way?
Our boy has lots of environmental allergies and his eyes constantly tear so we give Benedryl twice a day to help. Everything else you are doing is great.... You could also a product like Monkey butt or Desitin to sooth the raw skin, be careful not to get too close or in eye
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