Prednoleucotropin is a potent steroid. I'm sure it was prescribed for your dog to try and help shrink up the tumor and decrease the inflammation and stop the bleeding from the tumor. Major side effects of steroids include increased appetite, increased drinking, increased urination. But steroids can also cause excessive panting and make the dog just feel "weird." I suspect this is why he is having the rapid, shallow breathing.
It would be worthwhile to ask your vet about adjusting his dose. If you are currently giving the medication once a day, you could divide the dose and give it twice a day. That might help. If the bleeding has stopped, then you may be able to lower the dose of the pred. Pred does need to be tapered, so work with your regular vet on decreasing the dose gradually.
Being told by my vet that it was a double edged sword and could offer no other pills i have changed vets and he does not use the pills prescribed and is gathering the x ray results and blood tests together and i am seeing him Monday morning for new treatments. thank-you for your advise.