In addition to your mild sleep apnea, your secondary pulmonary hypertension may or may not be due to the rheumatoid arthritis. It is unlikely that your shortness of breath, tightness in the chest, and dry cough are related to the prednisone itself. Water retention can be a side effect of prednisone. If you have had a major increase in water retention this could cause your breathing symptoms. It is possible for rheumatoid arthritis to affect the lung and cause breathing symptoms. It is also possible for heart problems like the 3 floppy valves in your heart to cause breathing symptoms. You will need to check with your doctor to learn the cause of your breathing symptoms and the best treatment.
Prednisone will definitely help with pain from rheumatoid arthritis. There are also many other medicines that will help just as much. It is possible that the increased water retention and overall feeling of greater fatigue that you have noticed are side effects of the prednisone. If your pain persists, a rheumatologist would be the type of specialist to find the treatment that will help you the most with the least side effects.