I had JUST sharpened my knife last night and while slicing, I sliced into my left index and middle finger (the tips).......clearly, I was not tucking my fingers!

After stopping the bleeding (which took a while), I put Neosporin on them, and bandaged them. Today I'm continuing to do that, and changing the band-aids (those cool new fingertip band-aids!) every two hours or so....

Anything else I can do to heal them? They're not REALLY deep, I cut into the pink on both of them.....I'm hoping they will heal relatively quickly.

Advice?