thanks for query.
At present as there is infection, go for one antibiotic medicine course.
Apply some antibiotic cream on the lips.
Within few days your cracked lips will be alright.
Then do one thing,never lick or apply saliva on your lip as when saliva will be dried up and there will be chances of having crack again.
Leave habit of applying your saliva on the lips with your tongue.
Take some vitamin B.complex, folic acid
Apply some moisturizing cream or lotion on your lips.
Ok and bye.