You can get antihistamine eye drops over-the-counter in most drug stores. Try those to see if it helps. Pre-treat half an hour before he goes into the pool to see if it can prevent the symptoms.
Another thing is that chlorine is a strong irritant and may be irritating his eyes chemically. Chemical irritation has nothing to do with allergic reactions and thus would not respond to anti-allergy medications (such as Prednisone, antihistamines, etc.).
Has he been to an eye doctor to rule out eye diseases that may mimic eye allergy, such as dry eye?