Dry intermittent cough for 3 weeks with throat and chest tightness. I do not smoke. Not an issue when working out or sleeping. Starts a couple hours after waking up. Can pnd cause all of this?

Possibly. While it is possible that PND is causing this, PND typically does not cause a dry cough unless it is very little; also chest tightness seems odd in the scenario of PND causing your cough. An evaluation by a pcp and perhaps a chest x-ray would not be a bad idea.
PND. Yes your allergic nose can cause your aforementioned symptoms. Try taking an antihistamine at night and if need be one in the morning. Use salt water nose drops as well. Sleep with a vaporizer on several pillows. Use vaporub on your chest at night.
Cough. Pnd can definitely be the culprit if you have it. Allergy with PND or without can do it as well. Acid reflux is another common cause. To remove or lessen pnd, I use neti pot, humidifier in the room through the night if the environment you live in is dry. Acid reflux - prop the head of the bed, avoid overeating, tight belts, supine positions after meals, lose weight. Try Omeprazole or prevacid (lansoprazole).