hi there, usually the common cold
is caused due to some virus which persists for 5-7 days and gets cured on its own but it makes our body weak so that it is more suseptible to bacterial infection and so bacterial superimposed infection after a cold are quite common. You seem to be having the same problem and I think you will need a course of antibiotic like azithromycin
500mg twice a day for 5 days to take care of the infection,. you could also use steam inhalation and expectorant syrup to help you cough
out the phlegm. Take care.