Your baby has phlegm collection in the lungs which is making it difficult to swallow good and milk. The best way is to Nebulizer with Asthalin as oral cough Syrup cannot relieve the block inside the lungs.

Prolonged cough in such a small child may be due to multiple reasons. Gastroesophageal reflux, persistent pneumonia, recurrent upper respiratory infections, cystic fibrosis are a short list of possible causes. And there is a significant proportion of patients who have no identifiable underlying issue. Please discuss it with your pediatrician after re-examining the patient.