Herpes Simplex Virus (HSV) Infection: This is a common condition that presents with painful, stinging bumps or vesicles around the lips, often referred to as cold sores. The duration of 3 weeks could be consistent with a prolonged outbreak or repeated episodes.

Contact Dermatitis: An allergic or irritant reaction to substances like cosmetics, food, or other environmental factors could cause stinging bumps around the lips.
Eczema (Atopic Dermatitis): This chronic skin condition can cause itchy, inflamed skin that might appear as bumps, including around the mouth area.
Impetigo: A contagious bacterial skin infection that can cause red sores or blisters around the mouth, though it's more common in children.

Lymphoma or Leukemia Cutis: Although rare, these conditions can present with skin lesions, including around the mouth. Early diagnosis is crucial for effective treatment.
Sarcoidosis: This autoimmune disease can cause skin lesions, among other symptoms, and requires prompt diagnosis to manage systemic complications.
Infectious Diseases (e.g., Syphilis, Tuberculosis): Certain infectious diseases can manifest with skin lesions around the mouth, and missing these diagnoses could have serious health implications.

Perioral Dermatitis: A condition characterized by a rash around the mouth, which can include bumps, but its cause is often unclear and might be related to the use of topical steroids.
Giant Cell Arteritis: An inflammation of the arteries that can cause a variety of symptoms, including skin manifestations, though it's more commonly associated with headache and visual disturbances.
Melkersson-Rosenthal Syndrome: A rare neurological disorder that can cause facial paralysis, swelling of the face and lips, and the development of folds and furrows in the tongue, along with other symptoms.