Recently, I have been experiencing very sharp, electrical type pains in both of my armpits. What is this?

Electrical pain. Electrical type pain is usually neurological in nature. Given this pain is going to both of your armpits i would consider some type of spinal problem in the area of your lower neck or upper back that could be pinching on the nerves. It is possible to have inflamation of the armpit area bilaterally, hydradenitis although unusual. A poly neuropathy from diabetes or thyroid problem could also be poss.