Asthma exacerbation: Emily's worsening cough, fatigue, and general feeling of being unwell, despite using Symbicort and a recent course of prednisone, suggest an exacerbation of her underlying asthma. The improvement in breathing with prednisone but persistence of cough supports this diagnosis, as asthma exacerbations can present with cough as a predominant symptom.

Upper respiratory tract infection (URTI): Emily's concerns about an upper respiratory infection are valid, given her symptoms of a worsening cough and feeling generally unwell. URTIs are common and can exacerbate asthma or present similarly.
Chronic bronchitis: The chronic nature of Emily's cough, particularly if it has been persistent for 6-8 weeks, could suggest chronic bronchitis, especially if she has a history of smoking or exposure to irritants.
Gastroesophageal reflux disease (GERD): GERD can cause a chronic cough, and the fact that Emily's cough feels different from her previous breathing issues could indicate a different underlying cause such as reflux.

Pneumonia: Although less likely given the chronic nature of Emily's symptoms, pneumonia is a potentially life-threatening condition that must be considered, especially if her condition worsens or if she develops fever, chest pain, or shortness of breath.
Pulmonary embolism: This is a critical diagnosis to consider in anyone presenting with a new or worsening cough, especially if accompanied by shortness of breath, chest pain, or other systemic symptoms.
Lung cancer: In patients with a chronic cough, especially those with risk factors such as smoking, lung cancer must be considered, although it is less likely in this scenario given Emily's age is not specified and her symptoms have been relatively short-term.

Cystic fibrosis: This is an unlikely diagnosis given Emily's age and the fact that she has been managed for asthma, but it could be considered in the differential for chronic respiratory symptoms, especially if there are other systemic symptoms or a family history.
Sarcoidosis: A multi-system granulomatous disease that can present with respiratory symptoms, including cough, but is less common and would typically be associated with other systemic symptoms or findings on imaging.
Bronchiectasis: A condition characterized by permanent dilation of parts of the airways, which can cause a chronic cough, but is less likely without a history of recurrent infections or specific findings on imaging.