Hello,
I suspect from the sound of what you have told me that this may be feline asthma. That is why the cortisone worked so well.
Asthma is a recurring respiratory problem that occurs when the lung airways constrict due to stimuli which normally should not cause a reaction. With your baby's lungs being small for his body that will make things worse. Airways swell and inflammation can cause the muscles go into spasm leading to constriction. Coughing, and wheezing can be signs of feline asthma. At times only a chronic cough is the sign of Asthma, but it can turn into an acute asthmatic crisis if left untreated.
There are treatments that can be given that would help as it does in human Asthma. There are daily medications like Theophylline which has been proven effective as well as new medications that have just been approved. Joan Jav917
http://www.marvistavet.com/html/feline_asthma.html
The information and suggestions given are basic first aid measures. In an Emergency, Please Consult Your Veterinarian For Further Help. Joan