Same as Dibbs, in my experience it takes a while for the blood to congeal enough to prevent pressure relief.
I caught a fingr in between a door and frame a few years back. A night of pain and no sleep and a quick phone call to a friendly Quack who recommend the paperclip trick. I was reassured that it wouldn’t hurt because the paperclip would be cooled quickly by the nail/blood underneath before it got a chance to damage any nerves. Ten minutes later and I was holding a safety pin over the gas ring waiting for it to go red hot. MTFU and I pierced the nail. The relief was immense and there was no pain either, the nail and blood did cool it enough!
A couple of tips though, don’t use a needle or safety pin. Go for the paperclip. The larger diameter metal means that there’s a bigger hole for the pressure to be relieved out of. Also, you really don’t need to put much pressure on your nail.It’s like a hot knife through butter when the clip is red hot.
all the best Chap!