Thanks for your query. Cough
following a sore throat
may take some time to resolve. I presume that the treating doctor is also of the same opinion.
If your son is comfortable and is taking part in regular outdoor activity following this episode of infection, he can certainly resume his swimming lessons provided he does not over exert. It is best to start the lessons in a graded manner.
Swimming will not help in reducing the cough.
Wishing your son all the best.