Sound like nerve damage. Pinched nerve somewhere most likely. What part of the arm? Back of arm? I would have your family doctor take a look. Maybe you just strained a muscle but "tingling" and "pricks" is usually nerve.
The tingles travel up an down my body in the "back" parts ie. back of the arm, back of the leg. So yes the tingles also reach behind my arm. As for meeting a doctor, my parents believe it is not a big deal until it is life threatening.