Should I leave the band aid?

Okay so last night I sliced the side of my pinkie finger off and not wanting to bleed put rubbin alcohol and peroxide over it with a bandaid and went to sleep. Tonight before bed I took off the bandaid and now the area around the cut is all white and soft. So I thought I should go to bed without a bandaid because it stopped bleeding and it might heal better, should I leave the bandaid on? Can it get infected???