Is it possible to injure your brain, like a dai, by rapidly moving your head up and down but with no impact? i was headbanging ironically.

Yes. Mild TBI.: Many factors are involved in injuring your brain such as DAI (diffuse axonal injury). Many injuries to the head are closed injuries such as TBI (traumatic brain injury) which occurs with velocity moving of the brain within the skull. Spinal fluid functions to protect and absorb many of the movements and activities that stress the brain. If you have symptoms it would be advised to get evaluated