The most appropriate diagnostic test to perform next is methacholine challenge testing. This patient has a history of allergies and a family history of asthma, and he is presenting with paroxysms of cough. This presentation is suggestive of possible cough-variant asthma, in which reversible airway obstruction occurs but the primary presenting symptom is a nonproductive cough. Although a classic presentation of asthma on spirometry includes an obstructive pattern and a significant bronchodilator response (200 mL and 12% increase in FEV₁), this finding is not present in all patients with asthma. Asthma is a dynamic airway condition, and obstruction may not be seen at rest or in the absence of an exposure to the asthma trigger. In patients with clinical symptoms suggestive of bronchospastic disease (such as unexplained dyspnea or cough, as in this patient) but with normal spirometry, bronchial challenge testing may be diagnostically helpful. Bronchial challenge testing uses a controlled inhaled stimulus to induce bronchospasm in association with spirometry; a positive test is indicated by a drop in the measured FEV_1. Methacholine is a commonly used agent that induces cholinergic bronchospasm at low concentrations in patients with asthma.

Although this patient has a history of allergies and allergic rhinitis, it is not clear that the cause of his cough symptoms is associated with an allergic trigger. Allergy testing may be helpful in patients with allergies and asthma in whom treatment for specific triggers would be beneficial and in those whose symptoms are not adequately controlled with usual allergy or asthma therapies.

High-resolution chest CT (HRCT) is used to define the lung parenchyma in great detail and is useful in patients with suspected parenchymal lung disease. However, this patient has no suggestion of an underlying parenchymal disease, and HRCT is therefore not indicated.

Measurement of serum IgE levels may be helpful in diagnosing allergic bronchopulmonary aspergillosis (ABPA), a hypersensitivity reaction of the airways that occurs when bronchi become colonized by Aspergillus species. ABPA is characterized by recurrent episodes of fever, bronchial obstruction, and cough productive of brownish mucus plugs. This patient's presentation is not consistent with ABPA; therefore, serum IgE testing is not indicated.