Suggest Treatment For Chronic Cough And Fever In 3 Year Old Child

Hi, my 3 year old has been poorly with a cough for over a month we have been to the doctors and hospital both say his chest is clear, he now has a temp which is being controlled by Calpol but this has been going on for the past 7 days as soon as the medicine wears off his temp is back up, he s coughing at night mostly but I m wondering should I insist he has an X-ray as I m really worried this could be something else. He s also off his food but is taking fluids. Thankyou