You should drain the blood under your nail if it is causing severe, throbbing pain and is making you uncomfortable.
However if you're not having any pain with the blood under your nail then draining the blood is not necessary or not needed.
The blood under your nail is called subungual hematoma.
If you don't drain a subungual hematoma the subungual hematoma will eventually go away and resolve on it's own.
A subungual hematoma is a collection of blood underneath your toenail or fingernail.
The collection of blood underneath the toenail or fingernail can be extremely painful for an injury of its size, although otherwise it is not a serious medical condition.
Regardless if you treat the subungual hematoma or not it will eventually be reasorbed by the body and a new nail will grow out.
On average the nail takes 6 to 9 months to grow completely out.
Subungual hematoma drainage is not necessary if the hematoma is not painful.
If the blood is spontaneously draining from the hematoma, drainage is also unlikely to be of additional benefit.
Ice and elevate the area to reduce swelling, and take over-the-counter anti-inflammatories like aspirin, Advil, or Motrin for minor pain.
But the pressure generated by pooled blood under the nail can be extremely painful.