What is it called when you hit your elbow so hard you have this tingling/electric shock feeling?

Hitting Funny Bone: Your ulnar nerve wraps around the elbow and fits in a groove there. If you hit directly on the nerve you have the sensation you describe. This is called medically a neuropraxia.

Contused ulnar nerve: The ulnar nerve lies just below the skin on the inside of the elbow and if hit in just the right way, can get bruised/contused causing tingling/electric shock into the fingers.