Well you can drill it yourself, just make sure the drill bit is sterile (moving the drill bit by hand, coming into the top of the nail). Then put some alcohol on it and apply ointment. Repeat the alcohol and ointment for the next ten days. Done about the same self inflicted injury a couple times with a car door and hood. The drilling and relieving of pressure will cut down on the throbbing and allow you to sleep. Not bad, until you hit the layer of skin under the nail itself, but it is not that thick and under it is blood so you will be fine.
If you can not find a drill bit (small sucker for sure), a needle will do the trick. Just come in between the nail and the skin (along where the two meet, starting at the tip of the finger), it will hurt a bit more but the relief from the throbbing caused by the pressure will be more then worth it. From your picture there is a somewhat close spot of entry to the blood pointing up in the middle of the nail, aim for there.
Since it has been a few days, there will be some puss with the blood coming out, squeeze the hell out of it to make sure it is all out. Not pleasant either, but it either needs to be done or you live in extreme discomfort for a lot longer. The nail could be salvageable, but that is something time will tell.
If you can bend your finger as much as you do in the picture it is not broken,
That is my two cents on it, no need to see a doctor. GOOD LUCK!