Had a wood splinter in my finger, just removed it using a needle and tweezers

It was a small wood splinter, quite embedded.

I am worried I have increased chances of infection by using a needle from home & tweezers from the makeup box.

It's out but my finger is pulsing now. I put savlon cream onto it and then a plaster.

Have I done the wrong thing?
Will I need a tetanus booster?

It will be fine and no you won't need a tetanus booster for it. My husband is always getting them as he does quite a bit of joinery work.

I would not worry I have used Stanley blades and pliers before now.

A splinter is only a small break in the skin so chance of infection is small unless your working in an area of concern..

I work in a school and it was on a class wooden outside gate x