Pinky First Ever Infected Cut On 1 Year Old's Pinky Finger?

Infected cut on 1 year old's pinky finger? - pinky first ever

My 1-year, fell to the pavement and scraped and cut the little finger (the only place!). I immediately cleaned with soap and water, apply Neosporin and two cups. I could not meet because their fingers are too small strips, and it just took the cloth that covered them with. I've been using Neosporin everyday (3 days now), but the finger is swollen and red light. There are no red lines (what I know to give blood poisoning), and she has no fever.
The doctor's office is closed until tomorrow. Is there something I do in the meantime to help too? Is it normal that the Court will receive a bright red, while the cure. This is his first cut ever, I have nothing to compare.