Twisted arm doing backhandspring, popped, fingers tingle, hard to close them, sharp elbow pain behind & on top of elbow, no swelling or bruising..?

Fracture: Can have sustained a radial head fracture. This would cause your symptoms and yet not cause swelling or bruising.

Need to examine: It is not feasible to provide a meaningful opinion without additional history, physical examination and may be some imaging studies. It would be prudent to see your doctor or go to the emergency room of a nearby hospital.