Chronic Sinusitis: This is the most likely diagnosis for ongoing sinusitis that lasts four weeks. Chronic sinusitis is defined as sinusitis that lasts more than 12 weeks, but symptoms can persist for weeks before reaching this threshold. It is often caused by a combination of factors including allergies, anatomical issues, and bacterial or fungal infections.

Acute Bacterial Sinusitis: Although the duration of four weeks is longer than typical for acute bacterial sinusitis, it's possible for the infection to persist if not fully treated or if there are complicating factors.
Allergic Rhinitis: Allergies can cause chronic inflammation of the sinuses, leading to symptoms similar to sinusitis. If the allergies are not managed, the symptoms can persist.
Viral Sinusitis: Some viral infections can cause prolonged sinus symptoms, especially if there are underlying conditions that impair the immune system or if the virus is particularly virulent.

Invasive Fungal Sinusitis: Although rare, invasive fungal sinusitis can be deadly if not promptly diagnosed and treated, especially in immunocompromised patients. It requires immediate medical attention.
Tumor or Cyst: A tumor or cyst in the sinuses can cause persistent symptoms and, if malignant, can have serious consequences if not diagnosed early.
Granulomatosis with Polyangiitis (GPA): Formerly known as Wegener's granulomatosis, GPA is a rare autoimmune disorder that can cause sinusitis among other symptoms. It can lead to serious complications if not treated.

Sarcoidosis: A condition that can cause inflammation in various parts of the body, including the sinuses, leading to chronic sinusitis symptoms.
Eosinophilic Mucin Rhinosinusitis: A rare condition characterized by the accumulation of eosinophilic mucin in the sinuses, often associated with asthma and nasal polyps.
Primary Ciliary Dyskinesia: A genetic disorder that affects the movement of cilia in the respiratory tract, leading to recurrent respiratory infections, including sinusitis.