I got hit in the mouth last night and my top lip is swollen , mostly on the side and on the inside there is like a dark red bruise.

Ice for swelling: Applying ice topically is helpful to bring down swelling from trauma. It is best to use a barrier between your skin and the ice, like a paper towel or cloth, and leave ice on for no more than 15-20 minutes at a time.

Hematoma is: most likely. Boxers get this a lot but no lasting effects. Please check with your primary care doctor.