Angular cheilitishttps://en.wikipedia.org/wiki/Angular_cheilitis
Angular cheilitis is inflammation of one or both corners of the mouth. Often the corners are red with skin damage and crusting. It can also be itchy or painful.

Angular cheilitis is a fairly common problem, with estimates that it affects 0.7% of the population. It occurs most often in people in their 30s to 60s, and is also relatively common in children.

Angular cheilitis can be caused by infection, irritation. Infections include by fungi and bacteria. In the developing world, iron and vitamin deficiencies may be the cause.

Treatment ― OTC Drugs
Apply OTC antibiotic ointment to the lesions twice daily for several days. Recurrent eczema on the lips can be the main cause of cracked lips. In this case, treating eczema at the same time can prevent recurrence. In developed countries, malnutrition is rarely the cause.
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  • The main cause is chronic eczema and associated infection on the lips. Malnutrition is not usually the cause.
  • A relatively mild case of Angular cheilitis extending onto the facial skin of a young person (the affected area is within the black oval).
  • A fissure running in the corner of the mouth with redness.
References Differential Diagnosis of Cheilitis - How to Classify Cheilitis? 30431729 
NIH
The disease may appear as an isolated condition or as part of certain systemic diseases/conditions (such as anemia due to vitamin B12 or iron deficiency) or local infections (e.g., herpes and oral candidiasis). Cheilitis can also be a symptom of a contact reaction to an irritant or allergen, or may be provoked by sun exposure (actinic cheilitis) or drug intake, especially retinoids. Generally, the forms most commonly reported in the literature are angular, contact (allergic and irritant), actinic, glandular, granulomatous, exfoliative and plasma cell cheilitis.
 Cheilitis 29262127 
NIH