This question has been asked for a few decades. And it's a valid one. All sensation, including pain we feel, passes through our nerves as electrical signals. So it would sound right if an external electrical current interrupts a pain electrical signal. And many people before us tried to decrease an injection pain by applying electricity to the injection site.

Coulter devised a gadget that applied TENS electricity to an injection site. His gadget didn't get traction. Aside from being bulky, his device often increased the injection pain. I know because I tested it. 

Valero is another pioneer that tried to reduce injection pain. He combined the application of TENS electricity with vibration with a vibrating motor found in cell phones. I did not find any appreciable decrease in injection pain after using a Valero device. I combined TENS electricity with tapping. The results were great. So great that I spent 13 years perfecting the technology. My team developed Noodle, a hand-held, battery operated device that makes injections more comfortable gently, safely, and without chemicals within seconds. For more information, please visit here.