When the muscles around the thumb tightens or stiffens, a self-massage is a good way to relieve it. You can massage yourself by simply rubbing the area around the thumb. You may use a golf ball or a tennis ball and roll them over on a table. A vacant roll-on deodorant bottle can also be used.
Interlock the hands at the area between the thumb and the index finger and then, push the hands against each other. Thus, both hands will get stretched and are also massaged gently when at the same time not getting a lot of stress on the thumbs.