The flareups are definitely instigated by something; whether it is stress (release of cortisol which promotes histamine release causing a flareup), food, airborne allergens, or contact allergens, something is instigating the flareups. Because your child has an established fear of the water due to the previous problems (chlorine) it caused; although you've rid the water of the instigating culprit (allergen), his remembrance of the discomfort produces a great deal of stress for him which would bring about an eczema flareup. For this reason, you may just want to clean and apply the nutrient rich moisture to his skin only once per day for now.
There are still other environmental allergens that could play a major role as culprit that I have not addressed with you. Wool clothing is an eczema irritant. For this reason, 100% cotton clothing is the preferred fabric for eczema sufferers. Pet dander (if you have household pets) are also eczema irritants/allergens. These are some other things to consider.