What can I do about an allergic reaction to lip ring?

Remove it. Assuming it is really an allergy to the metal in the ring, you have only 2 choices. The better one would be to remove it. Reactions to metals can be treated with corticosteroids (cortisone-like) either topically or orally. To treat your problem you would need to see a physician and get a prescription. In general, surgical steel grade piercings are better tolerated, but not by everybody.