How do you get rid of a swollen jaw after being hit, in it?

Time and ice. The sooner you get ice packs in the area the better. A bag of frozen peas also works well. Once it has already swollen to its maximum, you want external heat to help reduce the swelling. You can also use anti-inflammatory pain medication such as advil, Motrin or aleve (naproxen). However, you should also see a dentist just to make sure nothing is broken or needs any other treatment or attention.