Although rare, chest pain and shortness of breath can be symptoms of psoriatic arthritis. These might happen when the chest wall and the cartilage that links your ribs to your breastbone get inflamed.Even more rarely, your lungs or your aorta (the large blood vessel that leaves your heart) could be affected.lthough rare, chest pain and shortness of breath can be symptoms of psoriatic arthritis. These might happen when the chest wall and the cartilage that links your ribs to your breastbone get inflamed.