Cough changed - retest?

3ish weeks ago DS’s class bubble was sent home and told to isolate after one of them tested positive for covid. At the same time DS came down with cold like symptoms, but the school wanted him tested too because of the cough. We all ended up with the same symptoms so all had to get tested, waited 5 days for our results which all came back negative.

DS and me have had a lingering cough since the cold. Both were kind of chesty and phlegmy coughs but not that persistent so I wasn’t really worried, until today when DS’s cough has changed to a being more persistent but still a chesty/wet sounding one.

Does anyone know if he’s likely to need another test? And if he does would they test him again with him having had a test so recently?