My cat has bad asthma. The vet gave him prednisone for about a year. It was the only thing that worked and it was great because it was so easy. Maybe a total of 6 injections every month or every other month. Guess what? At 15 years of age he's been diagnosed with diabetes because of that. I took the risk, gambled, and lost. Two weeks ago an angel of a cat I rescued died from diabetes complications.
If you move forward with this, be prepared for your cat to get diabetes. My cat dropped 4 lbs in 2 months and is very bony, but because I was caring so much for the other cat with diabetes I didn't notice so much. I've seen the horrors of what diabetes can do to a furry sweetie you love so much.
Please consider alternatives other than prednisone. I'm trying coconut oil, which seems to work. Serrapeptase works for me (I have asthma too). I also go to the doctor for inhalers, and give it to my cat to breathe in via an Aerocat-type inhaler (Space Kitty's is much better and cheaper off Amazon).