Infected cuticle/hangnail advice please?

A few days ago, my thumb nail ripped to the side and tore into the cuticle on its side. The next day it hurt to put pressure on it, and the day after that I noticed that a tiny amount of pus could be squeezed out. I soaked it in warm salt water and held a tea bag over it for a while then put neosporin on it with a bandaid. Its much better today and I will repeat the process tonight, but how long should it take to solve the problem? If it improves, do I still need medical attention?