Final answer:
The most appropriate intervention would be to begin antihistamine and decongestant therapy for a teacher with a non-productive cough.
Step-by-step explanation:
The most appropriate intervention at this time for a 37-year-old teacher with three months of non-productive cough and worsening at night and in the morning, along with other negative symptoms and normal physical examination findings, would be to begin antihistamine and decongestant therapy. The student does not exhibit any symptoms of bacterial infection, such as fevers, purulent nasal discharge, or chest pain, and the chest x-ray shows normal lung fields. Therefore, the most likely cause of the cough is postnasal drip caused by allergic rhinitis.