How long does a broken wrist take to heal?
Try doing lighter versions of things you want to do. Start with range of motion, going just past the level where it starts to be uncomfortable. Do the same with grabbing, twisting turning. I don’t see why your wrist keeps you from swimming, dancing or driving. Maybe you won’t be as good, but you should be able to do those activities. You may just have to push yourself a bit. When you do the exercises (several times a day, several reps), use heat before hand to loosen it and ice after to reduce swelling. I suspect that your fear of pain is keeping you from using it and a physical therapist can help that. Most people recover from a wrist injury just by using the wrist and hand. But some folks need a push.