How long does it usually take for a 8 month old to get over a cold my son has been sick for almost…

How long does it usually take for a 8 month old to get over a cold my son has been sick for almost three weeks now first week everyone in the house had stomach flu and was throwing up including my son we took him to the doctor said it was nothing just let his system flush it out second time we took him the vomiting stopped but he was sneezing very often coughing and had a really runny nose again they said it was nothing its now week three he sounds more congested than ever and the sneezing and runny nose has not stopped. What do I do?