Greetings patient,
Cracked, chapped lips with itchiness are very common and I personally also have it at times. Though there are multiple reasons of it from local, environmental to systemic, the major reason behind this dryness and exposure to harmful sunrays
I would suggest you to uses an antiseptic cream available in market as over the counter drugs like boroline and a lip balm sunscreen with SPF 45 atleast.
But if it doesnt heals visit a dentist or dermatologist ASAP.
Next Steps
antiseptic creame and lip balm with sunscreen
Health Tips
visit a dermatologist or a dentist if it doesn't heal