Possibilities... Persistent chronic non-productive cough is usually due to bronchospasm (due to any cause), post-nasal drip, gerd or a combination of these diagnoses. An evaluation by a doctor is needed for diagnosis since these all have different treatments. If you smoke, smoking cessation is needed to decrease airway inflammation.
Asthma. Asthma can cause both of those symptoms and you may need medication which requires a prescription.