Hi Kawai_cs,
I am sorry to read about what happened - it sounds like it must have been painful in the moment!
I've sliced a little into fingers a few times, even though I always follow the "rules" on knives, and it always has healed adequately.
As long as you use the Neosporin or an equivalent, and there isn't an infection, I think it will turn out fine. So don't worry about it!
Mvh,
Michael