Does a small cut need a doctor if it hasn't healed any since Thursday? Toddler fell while we were playing outside

I made a picture of it my profile pick, but toddler has a small cut and it doesn't seem to be healing.

I've been washing it twice a day with mild soap. I did put Neosporin on it the first day, but not since (been trying to let it dry).

Should I continue trying to treat at home, or is it time to have a doctor look at it?