Coughing is never normal in a cat. It's also important for you to advocate for your cat's health. A thorough veterinary exam is necessary, but your veterinarian doesn't live with your cat and many times, the exam that your cat gets is only as good as the information that you provide. Give your veterinarian information about how often your cat coughs or has difficulty breathing, as well as the circumstances under which this happens. Is it a rare occurrence or does it happen every day? Does your cat gag, choke, or swallow at the end of the cough? That might mean excess mucus, which is another sign that this may be asthma instead of hair balls. Can your cat play without have difficulty breathing, and if not, how soon after running or playing does the problem occur? Does your cat have difficulty breathing when sleeping or at rest. Unfortunately, there isn't a test that your veterinarian can do to make the diagnosis, so all this information is essential. If your cat has a history of sudden difficulty in breathing or has a chronic cough, your veterinarian will do an x-ray of your cat's lungs. You may be told that there are changes that look like "doughnuts" to the layperson.
Hopefully you cat does not have anything this serious. I have a cat that had pneumonia and I noticed something was wrong from him falling down and then panting like a dog would. I put my ear up to his chest and heard lots of congestion. I rushed him to the vet on an emergency basis and it was good cause the vet said his right lung has shut down and the left one was going. He would have died if I hadn't brought him in so soon.
Maybe it's just a upper respiratory infection. Cats are prone to those and I do remember my cats coughing with those as well. These are usually cured with a round of antibiotics. Hope all goes well at the vets and I helped you some.