Final answer:
The most likely diagnosis for the 15-year-old girl is pulmonary hemosiderosis, a rare condition characterized by episodes of alveolar hemorrhage and iron deposition in the lungs.
Step-by-step explanation:
Based on the symptoms and examination findings, the most likely diagnosis for the 15-year-old girl is pulmonary hemosiderosis. The worsening episodes of cough, wheezing, and bloody sputum, along with the presence of crackles on auscultation and diminished breath sounds on the left hemithorax, indicate a lung disorder. The chest X-ray revealing increased opacification near the right hilar region further supports this diagnosis. Pulmonary hemosiderosis is a rare condition characterized by episodes of alveolar hemorrhage and iron deposition in the lungs, leading to respiratory symptoms and abnormal radiographic findings.