Chlorine contact . Chlorinated water is very irritating and causes a lot of trouble for serious swimmers. Lots of swimmers get an irritant rhinitis/sinusitis and end up with frequent sinus infections. It's very drying and irritating to skin and numerous people also find they get rashes from frequent contact with pool water, or their eczema gets worse. Changing to a salt water pool can help somewhat.
May no be allergy. The chlorine in the pool water is an irritant. When the airways are irritated by chemicals like chlorine (others examples are cigarette smoke, strong perfumes, cleaning agents like bleach etc) they react with congestion, sneezing, runny nose and cough and some times with even more severe symptoms.