Constant dry cough in 4 yr old for >25 d

My 4yr old is on and off showing this- constant dry cough lasting for hours. Happening after certain eating food or sometimes for other reason. This sometimes increases from afternoon or evening. Had been showing doctors from last 25 days. Given Montair LC, Salbutamol, antibiotic (Refizil) course, Protussa...No relief. Now giving only Salbutamol as syrup, Motair LC and Salbutamol nebulizer rarely. Chest was found clear. Mucous is forming as he is sometimes throwing up the mucous. But the cough is not going completely. Now from yesterday afternoon, for last 8 h cough is persistant, and there is significant amount of wheezing. He is finding difficult to breath because of the cough. When not coughing, his breathing is laboured. Please advice. Has he developed asthma?