Hi..
Can understand your concern..
As per your complain dryness and cracking of lips after tooth extraction can be due to continuous rubbing and drying of the lips during the extraction procedure if the extraction took a longer time to complete there must be continuous rubbing of the lips leading to dryness and cracking..
You need not to worry and will get better soon..
You should apply a thick coat of petroleum jelly over the lips for maintaining lubrication as well as it locks the moisture in..
You can apply lip balms containing beeswax..
You can also apply ice packs over the lips as it improves blood circulation and will help in alleviating dryness and cracks..
You can also apply
aloevera gel over the lips..
Avoid using high chemical containing lip cosmetics as it can be harmful in case of cracked lips..
Apply SPF 15 containing lip balms while going in sun..
Scrub the lips using natural scrubs like oats mixed with honey and do gentle scrubbing of lips, wash and pat dry,do not rub the lips..
Avoid sucking the lips..
Drink plenty of water to maintain hydration..
Hope this information helps..
If you find the answer helpful kindly write a positive review and click on found this answer helpful as a token of appreciation..
Thanks and regards..
Dr.Honey Nandwani Arora..