Thanks for writing your query.
Your children are suffering from allergic bronchitis/asthma
. Due to exertion during swimming, bronchoconstriction
i.e. narrowing of air passage/bronchioles occurs resulting in reflex in the form of cough
Antibiotic donot play a role unless there is added infection.
In bronchial asthma
or in bronchitis, bronchodilators are needed as they dilates the constricted air passage and gives relief in cough.
Bronchodilators can be given in the form of rotacaps or inhaler as this route is safer and more effective.
Antiallergy medicines like levocetrizine can be given to decrease the allergic reaction
Get them examined by a Paeditrician and give medicines under medical supervision only.
I hope this is helpful to you.