How do you reduce lip swelling when its from a piercing?

New vs old. New piercing - ice. Old piercing - may be an infection - see a dermatologist!
Could be infection. My concern in this case would be bacterial infection or activation of a dormant cold sore (herpes simplex infection). It's possible swelling could result from an allergic reaction to products used on the site or even a component of the metal or other material the piercing object is composed of. A cold compress helps if it's simply a reaction to being pierced, but other causes might not be helped.