Sneezing is a sign of irritation or inflammation in the respiratory system, the same with coughing. While sneezing affects the Upper respiratory system, an irritation in the lower respiratory system will elicit a cough. Respiratory infections in cats are often referred to as Cat flu.
Sneezing can be caused by a simple nose tickle, a noxious smell like chemicals, specks of dust, foreign object in the air pathways, or an infection. In cats, sneezing can be mild when your cat is reacting to something around it, or could be severe if it is consistent and you notice a discharge from the nose.
Coughing is most often a sign of inflammation. It could be due to an infection (either viral or bacterial) or parasitic worms, especially heartworms. Like sneezing, allergies can also cause coughing in a cat as well as a foreign object in the respiratory system.
Sneezing and coughing may be normal in some cats (especially when caused by a non-infectious origin) and it is not productive (no discharges). But if you notice consistent coughing or sneezing in your cat lasting for a few hours into a day, you should consult your veterinarian. If your cat is showing other signs of weakness, weight loss, and appearing to be sick, there is most likely an ongoing infection and you should see your Vet. Immediately.
When you present your cat to the Vet, he will diagnose the exact cause of the cough/sneeze and will treat it accordingly. Cats are usually given the Cat flu vaccine to prevent common respiratory infections. It is given at 6 months of age after which a yearly booster is given.