Finger infection by my nail , what do i do?

Doctor: Go to the doctor for possible tetanus shot and antibiotics, depending on the cause of infection.

Paronychia/Onychia: Paronychia, a fancy word for small abscess near the base of the nail (as pictured here), and onychia is same thing but on either side of the nail. The treatment for most abscess is incision/drainage--get the puss out. Warm-salt-water soaks may allow this to pop itself and thus no incision needed. So, if you need help, consult doc. If you can do it on your own, more power to you. Good luck.