My 11 weeks have phlegm since birth?

hi my son is 11 weeks old and he has a phlegm in his chest since birth i had been to doc for 2 to 3 times she gave me antibiotics for 5 days but it didn't effect on him so she told me to stopped to dot gv him more he might be have allergy with weather or pollen allergy i m giving him steam but green tea nothing working properly he has congested chest not runny nose i want to know does anyone experience it?some times he has difficult to drink milk he is on milk does any kind of of am i eating is causing this problem?