If there is no fever then chances of allergic reaction, acidity
and reflux
and high eosinophil count are more. Common allergens causing these symptoms are pollen, mold, dust, pet dander. Streptoccocal infection is the most common bacterial infection and can cause nasal symptoms too. Indoor exposure to black mold can cause upper respiratory tract symptoms such as sore throat and cough with or without wheeze in otherwise healthy people.
Ideally you should consult a chest specialist.