What is the best way to get rid of swelling in my lip?

Depends: If swollen due to trauma, ice on and off and ibuprofen. If the swelling is from a non-traumatic source, you would need to be examined as to why it is occurring. When known, the cause should be treated. Allergy, infection, salivary cyst and a host of other reasons could be at play. Your dentist is always a good source of information and help. Good luck!