The most likely diagnosis is allergic bronchopulmonary aspergillosis (ABPA). ABPA is a chronic hypersensitivity reaction that occurs in response to colonization of the lower airways with Aspergillus species. It occurs most commonly in patients with atopic asthma or cystic fibrosis (CF). The resulting inflammation causes difficult-to-control asthma, impaired mucociliary clearance, destruction of pulmonary parenchyma, and bronchiectasis. Symptoms typically include severe and uncontrolled asthma, cough with expectoration of mucus plugs, and systemic symptoms such as low-grade fever and fatigue. Radiologic findings may be normal or may show recurrent infiltrates or evidence of centrilobular bronchiectasis. Patients will have immediate skin test reactivity to Aspergillus antigens; this is often used as an initial diagnostic test. Laboratory studies show peripheral eosinophilia (usually greater than 1000/µL [1 × 10⁹/L]), serum IgE levels greater than 1000 U/mL (1000 kU/L), and precipitating serum antibodies to Aspergillus. Treatment consists of standard asthma therapies and the lowest dose of systemic glucocorticoids that effectively controls symptoms. Antifungal agents may be warranted to reduce fungal colonization, and omalizumab may also have a role in therapy.

Cystic fibrosis (CF) is an autosomal recessive disorder causing abnormal chloride transport resulting in thick, viscous secretions in the lungs, pancreas, liver, intestine, and reproductive tract with associated multiorgan dysfunction, with the most prominent disease occurring in the lungs. Although an increasing number of cases of CF are diagnosed in adulthood, this patient has a long history of allergies and asthma, but not chronic respiratory infections or other evidence of multisystem disease suggestive of CF. This lack of consistent symptoms and her older age make CF an unlikely diagnosis in this patient.

Eosinophilic granulomatosis with polyangiitis (formerly known as Churg-Strauss syndrome) is an autoimmune small-vessel vasculitis that presents with peripheral eosinophilia and characteristically involves the lungs as asthma. However, it typically has additional manifestations such as purpura on the hands and legs and sensory or motor neuropathy. This patient does not demonstrate these findings.

Hypersensitivity pneumonitis is an immunologic reaction within the pulmonary parenchyma to a wide variety of inhaled agents. It may be acute, intermittent, or chronic and typically presents with cough, shortness of breath, and fatigue. However, this patient has no clear exposure history, and hypersensitivity pneumonitis is not usually associated with peripheral eosinophilia or wheezing.