Hello Repeated cough and cold is more commonly occur due to viral infection or allergic disorder.But if it is due to bacterial infection(diagnosed after thorough clinical examination and investigation) immunodeficiency must be ruled out. If fever is not associated each time with other symptoms and there is positive family history of allergic disorder;it is more suggestive of allergic in origin. Most of the time upper respiratory symptoms are associated with ear problem,irrespective of it s viral,bacterial or allergic. In allergic disorder montelukast/levocetrizine syrup along with nasal drops helps. I would suggest you to consult your pediatrician for proper evaluation and to find out whether it is really bacterial infection(for which antibiotic is needed) or something else. Regards