Arm or hand swelling may be caused by illnesses that are limited to the arm or hand, such as tendinitis, or by an illness that affects the entire body, such as heart failure. Swelling that occurs only in one arm or hand is usually due to a disorder of the arm or hand. Swelling that occurs in both arms or both legs is usually caused by an illness that affects the entire body. The body is more susceptible to swelling as it ages.