Acne: This is the most common condition that presents with a facial rash, particularly around the nose and chin. The presence of crusty lesions can be seen in more severe forms of acne, such as acne vulgaris or acne fulminans.

Perioral Dermatitis: Characterized by a rash around the mouth, nose, and chin, perioral dermatitis can present with crusty lesions and is often seen in young women.
Seborrheic Dermatitis: This condition can cause a rash on the face, particularly in the areas rich with sebaceous glands like the nose and chin. It may appear crusty and is associated with a red, itchy scalp.
Rosacea: While primarily known for causing redness and flushing, some forms of rosacea (like papulopustular rosacea) can present with crusty lesions around the nose and chin.

Lupus: Systemic lupus erythematosus (SLE) can cause a butterfly-shaped rash across the nose and cheeks, which may appear crusty in some cases. Missing this diagnosis could lead to significant morbidity due to the systemic nature of the disease.
Sarcoidosis: This condition can cause skin lesions, including those on the face, which might appear crusty. It's crucial not to miss sarcoidosis due to its potential to affect multiple organ systems.
Tuberculosis (Cutaneous): Though rare, cutaneous tuberculosis can present with facial lesions, including around the nose and chin. Given the potential severity of untreated tuberculosis, it's a diagnosis that should not be overlooked.

Demodex Folliculitis: Caused by the demodex mite, this condition can lead to a rash and crusty lesions on the face, particularly in the areas with high sebaceous gland concentration like the nose and chin.
Granuloma Faciale: A rare condition characterized by single or multiple brownish-red plaques or nodules, typically on the face, which can occasionally appear crusty. It's more common in middle-aged men.