I usually swim in a warm pool, then got a bad cough after swimming in a cold pool. the coughing stopped after going into the hot tub. what caused it?

Spasm: Cold water can cause a spasm in the wind pipe that will create a cough avoid cold water if it get worst see your doctor for proper evaluation bilsalamah inshallah

Asthma?: If you are a non-smoker, mild asthma triggered by cold temperature or chlorine in a swimming pool may be the reason for you cough. The use of a bronchodilator prior to swimming may be helpful.