Looks like I have an infected cut on my leg, how treat it without seeing a doctor?

See a doctor. If the cut is infected you should see a doc. The signs of infection are redness, swelling, warmth to the touch. The cut usually gets more and more painful rather than normal decrease in pain. You may run a fever. A small amount of drainage and minimal redness in a cut may not indicate an infection. If you are worried go to a doctor as an untreated infection can be a big problem.
Be careful. It depends on how "infected" it is. Some cuts, when infected, can be actually serious infections that can be life threatening. I would err on the side of caution and seek medical attention.