Hello and hope you are doing well.
Your symptoms of dry cough, runny nose and throat irritation could most probably be due to allergens. These are substances like pollen, dust, animal dander, certain foods, insect venoms and certain medications. Exposure to allergens causes a runny nose with a resultant post nasal drip where secretions from the nose go backward into the throat and irritate causing cough. You will need to consult your primary care physician for proper clinical assessment. In the meantime for relief from your symptoms you could do warm salt gargles and take OTC antihistamines.
Hope this helped and do keep us posted.