I slipped and cut off part of my index finger, about 1/3, what should I do with !

I slipped and cut off part of my index finger, about 1/3, what should I do with it?

I put it in milk, I don't know if why but it seemed like a good idea.

You should put the amputated part in a plastic bag, then put the plastic bag on ice. Then you should rush yourself to a major hospital's ER so that a hand surgeon can be consulted for a possible replantation. Keep in mind that replantations are not always successful and that rehabilitation is very difficult. Milk is good for knocked-out teeth, not body parts.