Allergic Bronchopulmonary Aspergillosis (ABPA): This condition is characterized by an allergic reaction to Aspergillus fungi, leading to symptoms such as cough, sneezing, and blood in sputum. The high IgE level (1200 IU/mL) and the presence of eosinophils in the nasal mucus smear (30 eosinophils/HPF) support this diagnosis. The normal chest X-ray (CXR) does not rule out ABPA, as it can be normal in early stages.

Asthma with Allergic Rhinitis: The recurrent sneezes, cough, puffy and itchy eyes, and high IgE level are consistent with asthma and allergic rhinitis. The presence of eosinophils in the nasal mucus smear further supports an allergic component.
Chronic Eosinophilic Pneumonia: Although less common, this condition could explain the cough, blood in sputum, and eosinophilia. However, the normal CXR and lack of systemic symptoms make it less likely.

Wegener's Granulomatosis (Granulomatosis with Polyangiitis, GPA): This is a rare autoimmune disorder that can cause respiratory symptoms, including cough and blood in sputum. Although the normal CXR and lack of systemic symptoms (e.g., weight loss, fever) make it less likely, GPA can be life-threatening if not treated promptly.
Tuberculosis (TB): Despite the lack of history of TB contact, TB can sometimes present with atypical symptoms, especially in pediatric patients. The presence of blood in sputum warrants consideration of TB, even with a normal CXR.

Hypereosinophilic Syndrome (HES): This is a group of disorders characterized by persistent eosinophilia and organ damage. Although the high IgE level and eosinophilia could suggest HES, the lack of systemic symptoms and organ involvement makes it less likely.
Churg-Strauss Syndrome (Eosinophilic Granulomatosis with Polyangiitis, EGPA): This is another rare autoimmune disorder that can cause respiratory symptoms, eosinophilia, and vasculitis. However, the normal CXR, lack of systemic symptoms, and absence of neuropathy or skin lesions make it a less likely diagnosis.