Nasal Septal Hematoma: This condition is characterized by a collection of blood in the nasal septum, which can cause pain, redness, and swelling in the nose, often mimicking the sensation of a broken nose. The symptoms described, such as redness and pain inside the nose and swelling on the bridge of the nose, are consistent with a nasal septal hematoma.

Acute Sinusitis: Inflammation of the sinuses can cause pain and pressure in the face, including the bridge of the nose, and can lead to redness and swelling. The pain inside the nose could be related to the sinusitis, especially if it's caused by an infection.
Nasal Fracture: Although the question mentions it "feels like a broken nose," an actual nasal fracture could indeed cause these symptoms, including pain, redness, and swelling on the bridge of the nose.
Allergic Rhinitis: This condition can cause nasal congestion, itching, sneezing, and runny nose, but in severe cases, it might also lead to facial pain and pressure, including the area around the nose.

Cavernous Sinus Thrombosis: A rare but potentially life-threatening condition that can arise from facial or sinus infections. It's crucial to consider this diagnosis due to its severity, even though it's less likely.
Meningitis: In rare cases, severe facial or sinus infections can lead to meningitis, an infection of the protective membranes covering the brain and spinal cord. Early recognition is critical.
Cellulitis or Abscess of the Face: Bacterial infections of the skin and soft tissues can cause redness, swelling, and pain. In the facial area, these conditions can be particularly dangerous due to the risk of spreading to deeper structures.

Wegener's Granulomatosis (Granulomatosis with Polyangiitis): A rare autoimmune disorder that can cause inflammation of the blood vessels and affect various parts of the body, including the nose and sinuses, leading to symptoms like those described.
Sarcoidosis: Another rare condition that can cause inflammation in various parts of the body, including the nose and sinuses, potentially leading to similar symptoms.
Relapsing Polychondritis: A rare disease characterized by recurring episodes of cartilage inflammation, which can affect the nose and lead to pain, redness, and swelling.