This could be a part of Cheilitis, which is a medical condition involving inflammation of the lip. Or a bad case of Chapped lips , a condition whereby the lips become dry and possibly cracked. It may be caused by the evaporation of moisture.
Lip balm can often provide temporary relief, though it should not be used extensively. One should avoid licking their lips as saliva contains the enzyme amylase, which can damage the already compromised lip tissue.
Honey can be used on the lips as a natural remedy.
Cheilitis is associated with many conditions from Vitamin B12 deficiency, iron deficiency anemia, be a symptom of allergies.can also be caused by taking the (retinoid) drug Isotretinoin (brand name Roaccutane).
Applying protective paraffin-based ointment (such as Vaseline) or lip balms to the lips is normally very effective. Also take Vitamin B supplements.
If nothing works you can have a biopsy done to find out the cause.
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.
For your underarms and neck - For standard non-hormone induced hyperpigmentations Hydroquinone usually reduces or removes hyperpigmentations very effectively. It is a bleaching agent. Also always use sunscreen/sunblock as dark areas on exposure to sunlight turn darker still. For some patients with severe hyperpigmentation,surgical and cosmetic intervention may help.
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.