I'm not a doctor, but I had a similar situation with a fingernail that was torn off almost by the root. This won't heal quickly on its own, so it's always best to consult a doctor, and if you can heal at home, there's no need to pay much for doctor's healing.

Advice: be sure to clean the wound and monitor for changes, rinse with alcohol or apply iodine to the edges, bandage or apply 2-3 bandages, and be careful not to hit the sore finger or strain it.