Right now if he is below 150 take a half unit off his dose. The antibiotics are only going to take care of infection. If the inflammation is from his asthma then that's different. Now my Maxwell has asthma also and he has been OTJ for 3 years. I just can't use pred to control it, he has an inhaler called an Aerocat and I give him Albuterol and Flovent through that so the steroids stay in just his lungs. Don't know if that is an option for you there but might be something to discuss with your vet.
Mel, Maxwell, Autumn and The Fur Gang.