Welcome to healthcare magic.
From your description, it seems to me that you have cheilitis
, an inflammation of the lips. Do you have the habit of licking your lips often? This is the most common cause of cheilitis. If so, please avoid it.
Drink sips of water through out the skin to maintain hydration. Use a lip balm, preferably petroleum jelly which srsls the moisture and apply every 3 hours.
Bet ovate cream can be used for 3-5 days only if it worsens. Antibiotics generally do not help.
Hope this helped you.