I really feel you on this, it is so worrying when the cough just keeps lingering no matter what you try. At one year old, it might be good to bring him to see the PD just to be safe, because sometimes a persistent cough needs a proper check to rule out anything like an infection or allergy. The PD can also advise on whether the medicine he is on is the right one for his age and condition. Hang in there, you are doing your best for your little one.