I Cut Myself While Shaving (inner Lip) And The Next

I cut myself while shaving (inner lip) and the next day the cut was very sore and tender. After a few minutes the pain faided and I was fine until I washed myself and totally forgot about the cut and it reopened. The next day it was filled with pus and hurt extremely bad. I continued to clean it and my mom told me to put neosporin on it and the next day the pus was gone. Any idea what it could be? Did my cut just get infected? I have never had an issue before I do however cut myself while shaving.