It would have been nice if you would have posted a picture over here but by your description I can make out that you have a septic wound. You must have got hurt on a splinter somehow in your finger and that is getting septic inside. You need to start antibiotics immediately and consult surgeon who will remove that splinter or if any kind of puss formation, for you.
Next Steps
start on antibiotics and consultant a general surgeon
Health Tips
warm foamentation of infected finger