Acute Bronchitis: This is the most likely diagnosis given the patient's history of upper respiratory infection symptoms, productive cough with green sputum, and the persistence of symptoms despite over-the-counter treatments. The symptoms are consistent with an infection of the bronchial tubes, which would explain the cough and feeling of not being able to take a full breath.

Pneumonia: Although the patient denies fevers, pneumonia could still be a consideration, especially if the patient's symptoms have persisted and include a productive cough. The green sputum could indicate a bacterial infection.
Asthma: If the patient has a history of asthma, the symptoms could be indicative of an asthma exacerbation, especially if triggered by a recent upper respiratory infection.
Chronic Obstructive Pulmonary Disease (COPD) Exacerbation: If the patient has a history of COPD, the current symptoms could represent an exacerbation of the disease, particularly if the patient has a history of smoking or exposure to lung irritants.

Pulmonary Embolism: Although the patient denies chest pain and other classic symptoms, pulmonary embolism can sometimes present atypically, especially in older adults or those with underlying medical conditions. It's crucial to consider this diagnosis due to its high mortality rate if missed.
Lung Cancer: Despite the patient's denial of a history of cancer, it's essential to consider lung cancer, especially if the patient has a history of smoking or exposure to carcinogens. Persistent symptoms despite treatment for infections should prompt further investigation.
Tuberculosis (TB): Given the productive cough and persistence of symptoms, TB should be considered, especially if the patient has been exposed to someone with TB or has risk factors such as immunocompromised status.

Cystic Fibrosis: This genetic disorder could be considered in a patient with persistent respiratory symptoms, especially if they are young and have not been diagnosed with another condition. However, it's less likely given the patient's recent onset of symptoms following an upper respiratory infection.
Bronchiectasis: A condition characterized by damaged airways, leading to persistent cough and sputum production. It's a less common diagnosis but should be considered if other diagnoses are ruled out and symptoms persist.
Sarcoidosis: An autoimmune disease that can affect the lungs, causing symptoms similar to those described. It's a rare diagnosis but should be considered if other causes are ruled out and the patient has systemic symptoms or findings suggestive of sarcoidosis.