Disclaimer: The information provided on this website is not and should not be taken as medical advice. You should always consult a veterinarian regarding your pet's health.
There are a few reasons why your cat could be coughing and breathing heavily. One of the most common is feline asthma, which is similar to human asthma. If this is the case, then your cat will need steroids in order to relax the airways and help him/her breathe better. Other reasons for these symptoms are a lung infection or possibly lungworms.
Just like when we have a lung infection (like pneumonia), if your cat has a lung infection, it will make him/her breathe heavily and cough. A sign that it could be this as opposed to feline asthma is that there will be a decrease in appetite. As well, your cat will be more lethargic and may have a temperature.
Coughing is also a sign of lungworms. The coughing can cause air sacs to rupture, which will result in breathing problems. A cat can get lungworms from eating infected prey, like lizards, snails and small frogs. If your cat is an indoor cat then this is highly unlikely. If it is lungworm, it can be treated with deworming medication.
Regardless of why your cat is coughing and breathing heavily, it is best to go to your vet as soon as possible. Your cat will most likely need to have an x-ray done on its throat and chest to get a clear diagnosis.