You have a paronychia. This is an infection that develops along the nail margin. Often in in people that bite their nails. Some will drain on their own with soaks in warm water. Most need to be gently drained. An easy procedure. But dont put off getting it taken care of because it can get worse.
It is possible, but less likely, you have an infection of the pulp or soft pad of the finger. This is called a felon. And the procedure to drain this is more difficult and uncomfortable and also require antibiotics.
Hope this helps.