I had a very small piece of metal shoot through the tip of my finger like shrapnel what should I do?

Try running hot water (as hot as you can take it for as long as you can bear) over your finger so the skin softens up, and it might push the "shrapnel" closer to the surface of the skin so it'll come out.

your nurse local at school will give you a tetanus shot. An emergency room will do the same thing.
To identify blood poisoning feel underyour arm pits and any bulge get to a hospital, as this can turn into life threatening death.
Yes you could be lucky but then again you only have one life and not 9 like a cat.
Jaw hurts then this is lock jaw. Emergency room.