"Allergic conjunctivitis" refers to the inflammation or irritation of the thin clear tissue covering the white part of the eye and the inner part of the eyelids, caused by an allergic reaction. Full definition
However, some forms of allergic conjunctivitis occur year round. (health.com)
Answer: I would really have to examine him to know for sure but this sounds like allergic conjunctivitis - steroid (with antibiotic) ointment placed in / on the eye works best for this - I didn't see that you have tried that. (1800petmeds.com)
It is usually not contagious in dogs and is usually allergic conjunctivitis. (1800petmeds.com)