Chronic Bronchitis: This condition is characterized by a persistent productive cough, often with brown or yellow phlegm, and is a common cause of chronic respiratory symptoms. The patient's symptoms of chest congestion, productive cough with brown phlegm, and shortness of breath (SOB) that have not improved over a few weeks align closely with chronic bronchitis, especially in the context of possible smoking or exposure to pollutants.

Pneumonia: Although the patient has been battling symptoms for weeks, pneumonia, especially if caused by atypical bacteria or if it's a case of walking pneumonia, can present with similar symptoms and may not always resolve quickly without appropriate treatment.
Asthma: Chronic asthma can lead to persistent cough and shortness of breath, and if not well-controlled, can result in prolonged symptoms. The presence of brown phlegm might be less typical but could occur, especially if there's a component of chronic bronchitis or another complicating factor.
Chronic Obstructive Pulmonary Disease (COPD): Similar to chronic bronchitis, COPD can cause long-standing symptoms of cough, phlegm production, and shortness of breath, especially in smokers or those exposed to lung irritants.

Lung Cancer: Although less likely, lung cancer can present with persistent cough, change in sputum color, and shortness of breath. It's crucial to consider this diagnosis, especially in smokers or those with a significant smoking history, due to its severe implications and the importance of early detection.
Tuberculosis (TB): TB can cause chronic cough, sometimes with discolored sputum, and shortness of breath. Given its potential for serious morbidity and the public health implications, TB should be considered, particularly in individuals who have been exposed or are from endemic areas.
Pulmonary Embolism: While typically presenting acutely, in some cases, pulmonary embolism can cause subacute symptoms, including shortness of breath and cough. This diagnosis is critical to rule out due to its high mortality rate if untreated.

Cystic Fibrosis: Although more commonly diagnosed in childhood, cystic fibrosis can sometimes present in adulthood with respiratory symptoms similar to those described, including productive cough and recurrent infections.
Bronchiectasis: This condition involves permanent enlargement of parts of the airways and can cause chronic cough, excessive sputum production, and recurrent infections. It might be considered if other diagnoses are ruled out and the patient's symptoms persist.
Sarcoidosis: A systemic disease that can affect the lungs, causing cough, shortness of breath, and other respiratory symptoms. It's less common but should be considered in the differential diagnosis if other causes are excluded.