Welcome to HCM
You have cough after EGD yes it can occur for few days but as you had procedure on 5th Nov. it is more than 20 days.
If is persisting for so long there may be some kind of Pneumonitis
so if it is troublesome then a X ray
chest may be done and see if there is some thing,as there is no fever or sputum it may not be franc Pneumonia
but a inflammation, or bronchospasm
Take steam inhalation and if still persist consult your treating Physician,and take prescription medicines and I hope it should improve in few days.
You have not mentioned was your EGD normal or some kind of re-flux of acid may present as chronic cough
If you are taking medicines for it please continue and avoid oily and spicy food and going to sleep just after dinner.