This may be related to temperature of water of the pool.I do not envisage any chemical reactions, while it is quite possible some algae or weeds in the water could elicit a pruritic response.
Best wishes.
I gather that this is a form of hives. They have got worse after each water aerobic class and now will not go away. Anti histamine have not helped.
I visited some hot thermal spas yesterday and lay in the water for ages with no bad side effects. So do you think the itch is caused by a chemical in the public pool?