Asthma: The patient's symptoms of coughing, wheezing, and sputum production, along with improvement in wheezing with albuterol (a bronchodilator), suggest asthma as a primary consideration. However, the lack of response to oral steroids is somewhat atypical and may indicate a more complex or severe form of asthma.

Chronic Obstructive Pulmonary Disease (COPD): Although less likely in a 41-year-old without a significant smoking history, COPD could present with similar symptoms. The improvement with albuterol supports this possibility, but the age and lack of mentioned risk factors make it less likely.
Bronchiectasis: This condition involves permanent dilation of parts of the airways and can cause chronic cough, sputum production, and wheezing. It might not respond well to typical asthma treatments, which aligns with the patient's partial response to therapy.
Allergic Bronchopulmonary Aspergillosis (ABPA): This is a condition that occurs in people with asthma or cystic fibrosis, caused by an allergic reaction to a fungus called Aspergillus. It could explain the patient's symptoms and the variable response to standard asthma treatment.

Lung Cancer: Although rare in a 41-year-old, lung cancer can present with cough, wheezing, and sputum production. It's crucial to consider, especially if there's a history of smoking or other risk factors, as it would drastically change the management and prognosis.
Tuberculosis (TB): TB can cause chronic cough, sputum production, and wheezing, especially if it involves the upper lobes of the lungs. The lack of response to doxycycline and steroids makes this a consideration, particularly if the patient has been exposed to TB or has risk factors for TB.
Pulmonary Embolism: While less likely to cause chronic symptoms, recurrent pulmonary emboli could lead to chronic pulmonary hypertension and symptoms like cough and wheezing. This diagnosis is critical to rule out due to its high mortality rate if untreated.

Cystic Fibrosis: Typically diagnosed in childhood, cystic fibrosis can occasionally present in adulthood with respiratory symptoms like those described. It's a rare consideration but important to rule out due to its significant impact on management and prognosis.
Eosinophilic Granulomatosis with Polyangiitis (Churg-Strauss Syndrome): A rare autoimmune condition that can cause asthma-like symptoms, along with eosinophilia and vasculitis. It's an important diagnosis to consider due to its potential for severe systemic involvement and the need for specific treatment.
Hypersensitivity Pneumonitis: An allergic lung disease caused by a variety of inhaled substances, leading to inflammation of the lung tissue. It could present with similar symptoms and might not respond to standard treatments, making it a rare but possible diagnosis.