In my experience although not with a little baby... i was swabbed and came back positive before i showed any symptoms, i then had antibiotics and never got the cough. the only issue i have had is the first cold since has been a doozy and the cough with it has been terrible, Which i have been told is somewhat normal after WC to suffer bad coughs from common cold due to the damage done to the cillia with in the lungs..
i aslo assume your doctor has put you all on antibiotics not just your DS? as you can still pass the bacteria on.