Angular cheilitis https://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, affecting about 0.7 % of the population. It occurs most often in people aged 30–60 years and is also relatively common in children.

Angular cheilitis can be caused by infection or irritation. Infections may be fungal or bacterial. In the developing world, iron and vitamin deficiencies may be responsible.

Treatment ― OTC Drugs
Apply an OTC antibiotic ointment to the lesions twice daily for several days. Recurrent eczema on the lips can be a major cause of cracked lips; treating the eczema simultaneously can prevent recurrence. In developed countries, malnutrition is rarely the cause.

#Polysporin
#Bacitracin
More information ― English
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