Based on the history you provided, below are the possible causes for your cat’s coughing. Please click on the links for more information on these diseases. If you still seek further information, please refer to our Ask the vet page to ask a veterinarian 24/7.
Asthma
Complications from Heart murmur
*At this age with a cough of this duration with no recent exposure to other cats, lung cancer also must be considered as a possible cause. Lung cancer in cats is often the result of spread of a primary cancer elsewhere in the body, however, cancer of the lungs can be primary. A veterinary visit for your cat is therefore recommended ASAP.