Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern..
As per your complain excessive peeling and dryness of lips that does not heal can be due to a condition known as Exfoliative Chelitis and is due to causes like bacterial [staphylococcus] infection,yeast infection,
mouth breathing, lip biting, lip sucking and lip licking habit,
nutritional deficiency etc..
I would suggest you to apply Tacrolimus and marigold containing ointment over the lips..
Always coat your lips with a thick coat of petroleum jelly or bees wax containing lip balm..
Avoid lip biting or sucking habit..
Keep yourself well hydrated..
In case if still there is no relief in 15 days
consult a Dermatologist and get evaluated and he can investigate your lips for infections and advise medications accordingly..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora..