Welcome to the wonderful world of the theremin, colonel. EXACTLY what you are describing has happened to many of us - every combination of carpal tunnel, tennis elbow, tendinitis, etc. etc. Here are a couple of rules for beginners - ignore them at your own peril!! 🙄
1. If anything hurts when you play your theremin (fingers, wrist, shoulder, even legs & feet) STOP PLAYING IMMEDIATELY and take a rest.
2. If you find after your first couple of weeks that any area of pain is either not going away or getting worse, you must change your playing technique. Never persist with a technique that causes problems in the hope that those problems will eventually disappear on their own. THEY WON’T. They will only get worse and become chronic.
I have observed over the last 20 or so years of playing the theremin that the methods that cause the most problems with the pitch hand, are those that involve thrusts of the wrist and extended fingers toward the pitch antenna. There are people (such as thereminist Carolina Eyck) who use these kinds of techniques with no problems, but others (like myself and several players in this forum) have had to find alternative methods of pitch control.
Clara Rockmore is considered by many to be the finest thereminist who ever lived. If you watch her play, you will notice that she never throws or thrusts her hand or fingers toward the antenna. Articulation is accomplished with knuckle extensions, while the fingers themselves remain comfortably curled and the hand remains in a straight line with the forearm, with no bending of the wrist. Vibrato is played by a movement of the entire forearm from the elbow (never from the wrist or by means of finger wiggles).
What sort of technique are you currently using that seems to be giving you problems?