Recurrent dry cough. Have. please help!

Hello doctors, so i have been experiencing dry coughs on and off for many months now. A slight exposure to dust or cat fur or even eating a bit of acidic food late at night (i have GERD), causes me to have a burning sensation in the throat followed by cold, cough and fever and i often follow up with medicines after which the cold and fever are treated but the dry cough remains. Recently too, after taking a medicine course which consisted of Augpen-LB 625 and other cough medicines, my coughing didn't reduce. After a follow up, the ENT doctor said that my issue isn't related to ENT and i must consult a chest physician. While coughing i feel like my throat and chest are vibrating. While i have been prescribed another course for 7 days (2nd attached picture), i wish to understand what my issue could be and what tests I must do to know what issue i have. Please help regarding this. Thanks!