Step 1: Identify the clinical pattern. A respiratory infection that initially improves and then relapses with worsening breathlessness, leaving a chronic obstructive picture, suggests post-infectious airway injury rather than a single acute illness.
Step 2: Interpret the chest X-ray finding of hyperlucency. Unilateral or patchy hyperlucency (the Swyer-James / MacLeod pattern) reflects air trapping and reduced perfusion in lung damaged after infection, classically seen in bronchiolitis obliterans.
Step 3: Interpret the pulmonary function test. An obstructive pattern indicates small-airway disease. Bronchiolitis obliterans is a fixed, post-infectious obliteration of the small airways producing exactly this fixed obstructive picture with air trapping.
Step 4: Exclude the alternatives. Alveolar proteinosis gives a restrictive picture with alveolar filling (ground-glass), not hyperlucency. Post viral syndrome is self-limited without fixed obstruction or hyperlucency. Asthma causes reversible (not fixed) obstruction and does not produce persistent hyperlucency on a plain film after a single infection.
Conclusion: The combination of post-infectious relapse, hyperlucency, and fixed obstructive PFT points to bronchiolitis obliterans. This matches the printed key (option A).