Hi, thanks for writing to HCM.
Finger pulp and nail bed injuries are very painful as that area is richly supplied by nerves. The blood clot under the nail will produce excruciating pain and may need drainage
Temporarily you can use ice compressions or wrap, keeping the finger in elevation, some analgesic
antiinflammatory medications will help.
I suggest you to have an orthopedic surgeons consultation to rule out any bony injury
. Hope this helps