Seborrheic dermatitis: This is a common condition that can cause a rash on the face, including the corners of the nose. It is characterized by a red, itchy, and flaky rash, often associated with oily skin.

Contact dermatitis: This condition occurs when the skin comes into contact with an allergen or irritant, leading to a rash. The corner of the nose is a common area for contact dermatitis due to exposure to allergens like nickel in glasses or irritants like soap or makeup.
Acne: Acne can occur on any part of the face, including the corners of the nose. It is characterized by comedones (blackheads and whiteheads), papules, pustules, and sometimes cysts.
Rosacea: This is a chronic skin condition characterized by flushing, redness, and visible blood vessels on the face. It can also cause small, red, pus-filled bumps, which may appear on the corners of the nose.

Lupus: Systemic lupus erythematosus (SLE) can cause a butterfly-shaped rash across the cheeks and nose, which may include the corners of the nose. Missing this diagnosis could lead to delayed treatment of a potentially serious autoimmune disease.
Sarcoidosis: This condition can cause skin lesions, including rashes on the face, which might appear on the corners of the nose. Sarcoidosis is a systemic disease that can affect multiple organs, making early diagnosis crucial.
Basal cell carcinoma: Although less common, skin cancers like basal cell carcinoma can present as a rash or sore on the face, including the corners of the nose. Early detection is key for effective treatment.

Sjögren's syndrome: This autoimmune disorder can cause skin rashes, among other symptoms like dry eyes and mouth. While it's less common for the rash to be isolated to the corner of the nose, it's a consideration in patients with other systemic symptoms.
Dermatomyositis: This is an inflammatory disease characterized by skin rash and muscle weakness. The rash can appear on the face, including the corners of the nose, but it's typically accompanied by other distinctive skin findings and muscle symptoms.

Treatment will depend on the underlying diagnosis. For example:

Seborrheic dermatitis and contact dermatitis may be treated with topical corticosteroids and avoidance of irritants.
Acne treatment includes topical retinoids, benzoyl peroxide, and possibly oral antibiotics for more severe cases.
Rosacea may be managed with topical metronidazole, azelaic acid, and oral antibiotics for moderate to severe cases.
Systemic diseases like lupus, sarcoidosis, and Sjögren's syndrome require specific treatments tailored to the disease, often involving immunosuppressive medications.
Basal cell carcinoma and other skin cancers are typically treated with surgical excision, topical therapies, or radiation, depending on the size, location, and depth of the tumor.