**Core Concept**
The patient's presentation is suggestive of an allergic reaction involving the respiratory system, specifically asthma, with possible eosinophilic involvement.

**Why the Correct Answer is Right**
The patient's history of allergies and recurrent episodes of upper respiratory tract infections, combined with physical examination findings of expiratory wheezes and use of accessory respiratory muscles, is consistent with asthma. The analysis of arterial blood gases showing respiratory alkalosis further supports this diagnosis. The peripheral eosinophil count is increased, indicating eosinophilic involvement, which is often seen in asthma due to the release of eosinophilic chemotactic factors from mast cells during an allergic reaction. The hyperresonant chest to percussion is also consistent with air trapping, a hallmark of asthma.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not account for the patient's history of allergies and recurrent episodes of upper respiratory tract infections. While bronchiolitis can present with wheezing and respiratory distress, it is more commonly seen in infants and young children, and is typically caused by viral infections rather than allergic reactions.

**Option B:** This option is incorrect because it does not explain the patient's peripheral eosinophil count or the presence of respiratory alkalosis. While chronic bronchitis can present with wheezing and respiratory distress, it is typically associated with a history of smoking and is not typically seen in children.

**Option C:** This option is incorrect because it does not account for the patient's history of allergies and recurrent episodes of upper respiratory tract infections. While chronic obstructive pulmonary disease (COPD) can present with wheezing and respiratory distress, it is typically associated with a history of smoking and is not typically seen in children.

**Option D:** This option is incorrect because it does not explain the patient's peripheral eosinophil count or the presence of respiratory alkalosis. While cystic fibrosis can present with respiratory distress and wheezing, it is typically associated with a history of recurrent pulmonary infections and is not typically seen in children with a history of allergies.

**Clinical Pearl / High-Yield Fact**
Asthma is a common chronic respiratory condition in children, and is often associated with a history of allergies and recurrent episodes of upper respiratory tract infections. The presence of eosinophilic inflammation is a key feature of asthma, and can be diagnosed using peripheral blood eosinophil counts or bronchoalveolar lavage.

**Correct Answer:** C. Asthma