Since when are you having the symptoms? What is your age? Do you smoke?
Some causes of the symptoms you mention, could be lip biting, lip licking, Vit.B2 deficiency, smoking, overexposure to sun and ill fitting dentures. In extreme cases, this could be due to bacterial or fungal skin infection.
You need to drink plenty of water daily – around 1.5 – 3 litres per day and eat a balanced diet. Do not keep your lips dry; apply lip balm which contains sunscreen – preferably a medicated one.
If you have cracks at the corner of your mouth it indicates B2 deficiency in this case you need to take B2 supplements.
If the symptoms still persist, consult your skin specialist or dermatologist.
Let us know about how you are doing and if you have any other doubts.