There are some medicinal options for treating hand arthritis. You can take pain-relieving medicines by mouth. There are also injections of steroid medicines to decrease swelling in the joints, and splinting to support and protect your hands.on’t forget about your wrists, which can also get sore and stiff from arthritis. To exercise your wrist, hold your right arm out with the palm facing down. With your left hand, gently press down on the right hand until you feel a stretch in your wrist and arm. Hold the position for a few seconds.