**Core Concept**
The child's presentation with recurrent fever, cough, and respiratory distress, along with a chest X-ray showing hyperlucency and pulmonary function tests (PFTs) indicating an obstructive pattern, suggests a diagnosis related to a specific type of infection that affects the lungs.

**Why the Correct Answer is Right**
The child's symptoms and test results are consistent with **Bronchiolitis**, a common lower respiratory tract infection in infants and young children. The hyperlucency on chest X-ray is indicative of air trapping, which is a characteristic feature of bronchiolitis. The obstructive pattern on PFTs is due to the inflammation and edema of the small airways, leading to airway obstruction. The recurrent fever and productive cough in the second episode suggest a possible secondary bacterial infection.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is likely a distractor, as there is no strong evidence to suggest a diagnosis of pneumonia in this child, given the absence of consolidation on chest X-ray.
**Option B:** While viral infections can cause respiratory distress in infants, the specific combination of symptoms and test results in this case makes bronchiolitis a more likely diagnosis.
**Option C:** **Asthma** is a possibility in infants, but the age of the child (3 months) and the absence of a history of allergies or atopy make this diagnosis less likely.

**Clinical Pearl / High-Yield Fact**
Bronchiolitis is often caused by viral infections, such as respiratory syncytial virus (RSV), and typically affects children under the age of 2. In severe cases, it can lead to respiratory failure and the need for mechanical ventilation.

**Correct Answer: C. Bronchiolitis**