What Causes Persistent Productive Cough In An Infant?

hello my son is 1 year old and he had a recent cold in the beginning of january. he is over is cold but still has some runny nose and a cough that wont go away i took him to the doctors becuase this wet cough as lasted for more than 2 weeks and he said that it is phelgm that is left over from the cold and at his age he cant spit it out but it will eventually go away. i tried vapor rub, liquids, humidfier. i dont want this phelgm to turn into pnuemonia. i need help please