Best treatment for a splinter?

I noticed a bump today on my finger that looked infected. I squeezed it and some puss came out. Whee! I squeezed again and some piece of splinter came out which I nipped with the tweezer.

Now, it still has some residual puss in there and it hurts a bit when I apply pressure. Is there a doctor in the house?

What’s the next step? I am using peroxide to sterilize the wound and I think it helped push the splinter piece out.