I had a tetanus shot the day b4 thanksgiving because I cut my thumb open and had 9 stitches. Now I have pain in the arm and can't move it much..

Pain in the hand, . Going up the arm, with swelling and redness is sign of an infection from a cut in the finger and treatament should be sought immediately. Pain in the area of the tetanus shot can be from a local reaction but can also mean that the area is irritated too much. In either case or if both pain that limits motion in the arm after a laceration in the thumb is not normal and you need follow up care now.
Go back to doctor. I had same problem with a patient. The shot was given by a nurse from another clinic. The pain and inability to move was from hitting a nerve on the injection site and had nothing to do with infection or the cut nor the medicine given. Have it examined and work up can be done.