Swelling and Pain. If your experiencing swelling, pain, decreased range of motion or anything out of the ordinary for you and it lasts more than a few days then get it checked by your doctor. Use the rice method to help- rest, ice, compression and elevation. Your whole hand's function is dependent on your thumb. If your thumb doesn't work, neither will your hand. I would get an x-ray if not better in 3-5 days.
It hurts to move it. Pain from a broken bone feels unstable. It feels like it hurts to move and you become afraid that it would hurt if you did move. A broken thumb would give you pain to open you hand or grasp or squeeze with it. But as with the last question i answered, you can settle all the concern with an x-ray.