Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain you seems to be suffering from Exfoliative chelitis and discolouration seems to be due to post inflammatory 
hyperpigmentation due to continuous peeling and inflammation..
Exfoliative Chelitis is a condition in which there is continuous peeling of the lips leading to appearance of dry, damaged and flaky lips..
It commonly occurs due to habit like lip biting, lip licking, lip sucking etc..
Other causes can be 
mouth breathing, bacterial and fungal infections..
As you are not confirmed that you have Exfoliative Chelitis or not you should 
consult a Dermatologist and get evaluated and he can do a clinical evaluation and investigations like microscopic examination of scraping from the lips can help in diagnosis..
In case of Exfoliative Chelitis you can be advised to apply a thick coat of Petroleum jelly over the lips..
You can also apply beeswax containing lip balm frequently throughout the day..
You can also apply Tacrolimus and Marigold containing 
ointments..
You should avoid licking, sucking or biting the lips..
Drink plenty of water.
In case of Bacterial or Fungal infection antibiotics or antifungal medicines can be given accordingly...
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.