Blood blisters on the fingertips need to be lanced to relieve the pressure. Heat a pin/needle under a flame (lighter will do) then lance the blister and squeeze the blood out, you may have to do this a few times if the blister has pockets.
You can use an ice cube to free the area, just wrap it in a cloth, do not put the ice direct to the skin.
All that has happened is you have trapped the skin either in compression or tension an the impact has not broken the skin. Blood and fluids fill up the void and you feel the pressure of this.
Our hands's, and in particular out fingertips, are full on nerve endings, so it feels worse that other parts of the body because they are more aware of the damage. We are more aware of it because of the extended use we have for our hands in life, we take for granted our hands, but when constant pain in doing routine tasks is there we are constantly reminded of our little injury.
The same applies to the fingernail, if injured the best way to relive it is 'drill out the nail' to relieve the pressure.
Again there are many ways to do it, yes it hurts, but once done you not only relieve the pressure and the pain, you also stand a better chance of saving the nail.
Again heat up a sharp lance (fine drill bit, point of a knife or stiletto)and slow rotate it back and forth making a hole in the nail till you relieve the pressure.
Again you can use ice as before to freeze the injury.
But now you can rest the fingertip on the ice to keep it cold, so relieve the pain as you drill.
Do not use a power tool as you may not control the depth and do more damage. Be aware that the blood will come out is a spurt as it is under pressure, it can easily hit your face in get in your eyes.
In both cases bathe with antiseptic, keep them clean. One the hand or finger a small dressing can be used when at work, but remove when at home. On the nail just use some super glue over the hole and let the hole grow out.
Use care, caution and your own sense of pain in these matters and if you feel the need see a doctor or medical professional.