It is called "panting" and part of any serious training for singers and wind players. It must not be done with the chest, but with the "belly" (or diaphragm). The reason why it is called "panting" is that if your pants are too tight, it won't work ;-).

Breathing using the diaphragm is generally considered healthy - I always do it. Don't exaggerate the panting, though. Also, you wrote that you have medical problems with your respiration; before you do any serious training, you should ask your doctor.