Chlorine is a commonly used pool water disinfectant. When chlorine combines with sweat, urine, and other contaminants, it forms a compound called chloramines — which saturate the water, move into the air space, and can irritate a number of body areas, including the throat.
A properly functioning water filtration system and a ventilation system that cycles fresh air into the pool area can minimize the presence of chloramines. The CDC also recommends showering well before getting in the pool and taking regular restroom breaks to minimize the amount of urine in the water; these precautions can help reduce the level of chloramines.
I recommend talking to your health care provider about your symptoms. If you determine that the pool is the source of your irritation, you may need to forego water exercise, limit your time in the water, or find another pool with better maintenance practices.
It wouldn’t hurt to ask your pool manager about the ventilation system and if increasing the level of fresh air moving in and out of the pool area is possible.