Tears from your eyes while coughing is a natural phenomenon due to occlusion of the naso lacrimal duct opening to avoid regurgitation. So don't need to worry about it.
environments will make the air dry and your mucus thick,which drips down the throat and tickles it causing a cough reflex. Or it could be due to allergy
also. Try using a humidifier and switch it on at least 10-15 mins before you enter the room and avoid dusty areas as a precautionary measure.
Get your nasal sinuses
examined for any chronic sinusitis
. Take care.