It is is usually cortisone injections. You need an orthopedist/surgeon that specializes in hands. Make sure you ask around about how good they are… reviews are nice, but asking people you know is better.
Thumb problems are usually either bone on bone arthritis or trigger thumb. I had both. With trigger thumb you will have a clicking or catching when you use your thumb. With bone on bone if you press on the joint at the base of the thumb.. near the wrist it will be very tender, maybe swollen. I had pain when I pinched my finger together or tried to hold a pen. Not sure which one caused that.
Trigger thumb is a tendon problem. The fix for it is a surgery that last total of about 20 minutes from time they take you back to OR for prep and closure of cut. The surgery is basically a tendon release.
The surgery for the arthritis varies as to which procedure they use. The bone is removed and an implant placed, another they use a tendon to fill space, and the tightrope.. which I had. With the tightrope they place a string.. much like fishing line.. between thumb and index finger. The space where the bone is filled in with debris, blood and eventually scar tissue.