Best way to treat a swollen lip?

Ice then heat: Within the first 3-6 hours, use ice pack. Then after 12 hours use moist heat pack.

From what?: If it's swollen from trauma, use ice pack first 24 hours on and off every 15 minutes. Then it's just a waiting game until it goes away. If of unknown origin, you need to see a dentist as soon as possible as it is likely an infection that would require immediate treatment.