I am sorry to hear that Mica has labored breathing the past two days.
A normal cat has a resting respiratory rate of about 10 to 15 breaths per minute, and one breath is considered the in and out motion of his chest. If he has a rate faster then 40 breaths per minute then he is in trouble.
Allergies usually cause itchy skin, not breathing difficulties.
While asthma can cause labored breathing and is generally responsive to steroids there are many other things that can cause labored breathing. And some can be made worse with steroid use.
If he doesn't have a nasal discharge and isn't sneezing then his difficulty breathing is likely related to a problem in his chest or secondary to anemia (decreased numbers of red blood cells).
Problems in his chest leading to an increased respiratory include primary heart disease (including cardiomyopathy and heartworm), lung disease including asthma, bacterial, viral, parasitic (lungworm) or fungal infections, a mass(es) in the chest including lymphoma, heart based tumors or carcinomas, or fluid around the lungs (pleural effusion) due to a mass, bleeding, chylothorax or an infection.
Anemia can be secondary to poor red blood cell production, either due to kidney disease as the kidneys make a hormone to stimulate production or primary bone marrow disease, or anemia can be due to bleeding or destruction of red cells due to a tumor, blood parasite or autoimmune disease (body attacks its own red blood cells and destroys them).
If your fellow's tongue and gum color are a nice bubblegum pink them he is in better shape then if his gum and tongue color is blue or gray, these would signify he is real trouble and this is a true emergency.
The conditions I listed above are serious and I would highly recommend that your fellow see a veterinarian promptly to have an examination and further testing done based upon his examination before any more prednisone is given.
Mica likely needs radiographs of his chest to evaluate his heart and lungs to start and then further diagnostics based upon those findings. That may include testing for heartworm and lungworms, aspirating fluid for examination if there is fluid present around his lungs, or blood titers for fungal infections.
In the meantime keep him quiet so he can breathe as easily as possible.
Please let me know if you have any further questions.