It sounds like a paronychia. Soak in warm water and soap several times per day. If persists, or redness begins moving toward the top joint in the finger, see a doctor. The doc may need to open up a small area of skin to drain it, and then put you on an antibiotic.
http://www.webmd.com/a-to-z-guides/paronychia-nail-infection
Wow. What a nasty infection that can be.