Did your veterinarian test for heartworms in your kitty?
I agree with Tom. Please test for heartworms. A cat that is negative for heartworms may still have heartworm associated respiratory disease though. In a recent study, 30% of the cats positive for heartworms were reported to be indoor only cats - so all cats are susceptible. A heart ultrasound would also help diagnose the problem and determine the best treatment. This heart ultrasound can also look for hypertrophic cardiomyopathy (HCM)- a common heart problem in cats. Our office cat developed signs of this at age 8, but not much cough was present at that time. Chest xrays are also beneficial to know, as they look at the lungs and the heart, but cats with HCM have normal hearts on xrays. Respiratory problems can be serious, so please try to see a veterinarian very soon. I wish the best for your kitty.