Rosacea: This is a common condition characterized by redness, inflammation, and sometimes pimples on the face, particularly on the nose. The absence of fever and mucus, along with the location on the bridge of the nose, makes rosacea a plausible diagnosis.

Contact Dermatitis: An allergic reaction or irritation from substances like makeup, sunscreen, or glasses frames could cause redness and pain on the bridge of the nose.
Acne: Although less common on the bridge of the nose, acne can occur anywhere on the face and could present with redness and pain.
Irritant Dermatitis: Similar to contact dermatitis but caused by non-allergic substances that irritate the skin, such as harsh soaps or sanitizers.

Cellulitis: Although less likely without fever, cellulitis is a bacterial infection of the skin that can present with redness and pain. It requires prompt antibiotic treatment to prevent serious complications.
Lupus: Systemic lupus erythematosus can cause a butterfly-shaped rash across the nose and cheeks, which might initially be mistaken for a more benign condition. Missing this diagnosis could lead to significant morbidity.
Sarcoidosis: This condition can cause skin lesions and might present with redness and swelling on the face, including the nose. It's crucial to diagnose sarcoidosis due to its potential to affect other organs.

Granuloma Faciale: A rare skin condition characterized by single or multiple, reddish-brown, bumps on the face, particularly on the nose. It's benign but can be disfiguring.
Nasal Furuncle or Carbuncle: A boil or group of boils in the nasal area, which could cause significant pain and redness. While not extremely rare, these conditions are less common than other diagnoses listed here.
Erythema Elevatum Diutinum (EED): A rare skin condition that can cause red, purple, or brown lesions, typically on the hands, feet, and face, including the nose. It's associated with various systemic diseases and infections.