Even a clean 1/16 drill bit in your fingers will bore a hole and it will feel 100x better with the pressure off.
I'm really reluctant to recommend anyone do "bathroom surgery"... the finger, nail AND drill bit all have to be surgically clean, not just wiped off on your pants!
The best tool I've ever used to trephine (the technical term) a fingernail or toenail is essentially a fancy disposable soldering iron. It has a plastic sleeve containing a couple of batteries, and a tiny filament tip. Hit the button, tip heats orange, burn through the nail, blood comes out (sizzles on tip), patient feels better immediately.
It only hurts them if you are careless and go too deep. The fingernail has no nerves - but the nail bed and fingertip sure do, and are already angry.
(It's also silly to make them single-use. Nothing infectious could survive the 1700F temp).
