When cats are sneezing or coughing, the first thing I would relate it to is the so-called kitty flu, but sometimes it may be caused by a different culprit. Did you know that asthma also happens to cats in various degrees.
Asthma in cats is a chronic inflammation of the small passageways of the lungs (bronchioles). When your pet has asthma, these passages thicken, and collapse when the cat inhales, making it difficult for the pet to catch its breath. - Dr. Ron Hines
Dr. Ron Hines shares his insight about cat asthma in his article: Feline Asthma - Chronic Bronchitis In Your Cat