Frequent cough and cold. Treatment?

Sir my two and half year old child catches cough and cold frequently (once in a month). the child is premature and had bronchitis last year. up to yesterday evening he had mild cough and after evening it has raised. No fever, last night we have given asthalin syrup and he had vomited food along with light cough. last month only we have used anti biotics for three weeks (Cefpodoxime, Clarithromycin, Ondansetron), after a gap of fifteen days again he got cough. Any kind hearted doctor please advice me permanent solution to his cough and cold. I suspect problem is in his lungs or he has low immunity. But how can we confirm and give correct treatment? Please help me out. we as a parents and child, suffering from two years with this cough and cold.