try to use hot tub, see if he is allergy to it. since the hot tub may use different chemicals than chlorine. most time he may allergy to combined chlorine, not the chlorine(since you didn't say he is allergy to tap water or bath, they all contain colorine.). if it the case for allergy to combined chlorines, goto different pool, find a one which have less smell(combined chlorine have smell, chlorine not; chlorine kill germs, combined chlorines not).
other choice, wash it out after swim, and use lotion...