What Is The Treatment For Swollen And Painful Toe?

I have a huge cut on my big toe. I have had a band aid on it for the last 3 weeks and, per the doctor i was, have not gotten it wet either. Will air help it heal? It is turning white from the antibacterial cream and a bit yellow around the area, is that normal? How do I know if it is infected or just healing? I have a very small spot underneath the nail at the corner of the nail where it is cut. It is very small, but should I be worried? Will the toe darken and fall off on it's own because of the trauma above it? The inside part closest to my next toe has a small cut as the would extends there. It is closing, but now that skin is closing over it it looks a little swollen right in that area, is that okay?