Yes, a lot of what you are describing are signs of chronic Prednisone therapy - muscle wasting to the belly, a pot-bellied appearance, an enlarged liver as Dr. Coyner stated, increased thirst/appetite/urination/panting, etc. I'd start with a thorough physical exam at your vet, and some blood work (he'll likely have increased liver function tests - ALK PHOS) from being on chronic prednisone. They can also do x-rays or even an ultrasound if necessary to see what's going on with the abdomen.
If he truly has COPD, it's imperative to keep him "skinny" and his weight down - extra weight is a large amount of strain on the heart and respiratory system (resulting in pulmonary hypertension or "cor pulmonale."). Good luck!
Potential causes for abdominal distention include an enlarged liver (due to prednisone), a mass/tumor, or fluid accumulation in the belly. An xray can be performed to find the cause for the swelling. You may want to consult with an internal medicine specialist (go to www.acvim.org to find one in your area, or ask your veterinarian for a referral) for other options to help his respiratory disease which may not have as many side effects as prednisone.
Good luck,
Kimberly Coyner, DVM DACVD