I slammed my finger in a draw now its blue and completely numb. its not broken i can move it?

X-rays: I suggest you do X-rays to check for bone cracks,if found clear,doctor will subscribe pain medication,putting ice on your finger might be helpful in recovery.

Neuroapraxia: You caused a bruising of the digital nerves resulting in a neuroapraxic injury to the nerves. This will resolve with time but will cause numbness until that occurs. The blue is result of bruising and echimosis if finger is also cold and has poor capillary refill may be a digital artery injury. Motion does not rule out a fracture you need to get an X-ray based on description of the finger.