The most likely diagnosis is a bronchial carcinoid tumor. This patient presents with evidence of airway obstruction with a likely postobstructive pneumonia. This should be suspected in patients who have a persistent pulmonary infiltrate and a localized wheeze on examination. Although bronchial carcinoid tumors represent only a small percentage of all lung cancers, they are the most common lung cancer in children and adolescents. Most bronchial carcinoid tumors involve the proximal airways, so patients may present with symptoms related to endobronchial narrowing or obstruction, including postobstructive pneumonia. Only approximately 1% to 5% of patients present with symptoms of carcinoid syndrome. Other endobronchial cancers should be considered in older patients. Foreign body aspiration or airway strictures may also lead to airway obstruction.

Patients with allergic bronchopulmonary aspergillosis can present with recurrent asthma exacerbations in the setting of peripheral eosinophilia, elevated serum IgE levels, and bronchiectasis. Thick sputum can result in airway obstruction with associated atelectasis. However, patients typically respond to systemic glucocorticoids rather than antibiotic treatment, as in this patient. In addition, she has no evidence of peripheral eosinophilia.

Chronic eosinophilic pneumonia is associated with peripheral and upper lobe–predominant areas of consolidation that improve with glucocorticoid therapy. Antibiotics would have no effect on the course of the disease.

Patients with cystic fibrosis can present with recurrent respiratory infections in the setting of bronchiectasis. However, this patient's chest radiograph showed no evidence of bronchiectasis.