Why is part of my bottom lip numb after I got hit in the mouth?

You pinched a nerve. The hit caused a small bleed under the skin in the area of the nerve. Once it gets better, the nerve will go back to normal. Take a vitamin B complex once a day. It helps nerves heal. I know that it's the bruise that pinched it off, but with a shortage of blood due to nearby swelling, there might be a tiny bit of damage. It will heal on its own, but it will heal faster with a B complex.