What could this be considered as? I accidentally broke a wine glass at work while polishing, and jammed the glass stem into the center of the palm of my hand. I instantly felt nauseous and shooting, electric like pain through my hand, arm, and middle fin

It . It sounds like you suffered some nerve damage from the trauma. It can take many months for the nerve to regenerate and repair itself, and there are cases where this does not occur. I dont see anywhere in your post a mention of a doctor's visit. If not, you should see one right away. You may still have glass in your hand which is causing your symptoms, or another issue that can be easily addressed with surgery or minor procedure.. Also there are medication treatment options available for this type of nerve pain. Best of luck.