I've been working out at the gym and my wrist is killing me (there's no bone fractures), what should i do and how long will it take to recover?

Professional: see if you can have a professional from the gym instruct you. If your wrists are hurting you may need to improve on your form. You may be lifting incorrectly. This will lead to excess stress on the wrist and not on the muscle. Long term proper form will reduce the chances of injury. For the pain you can try non steroidal. But make sure to take with food.