L.A.
considering it is at night and this time of year and the fact he is on Zyrtec already... there is a good chance he has COUGH VARIANT ASTHMA. Is it a dry non-productive cough? I have asthma where my attacks are just coughs like that, as do two of my children. Cough medicine won't make any difference - have you noticed that? Many doctors won't diagnose a young child with asthma, especially if they are having coughing rather than normal attacks. They may say he has reactive airway disease... basically asthma for tykes. If you are really concerned, talk to your pediatrician or an allergy doctor. We use Dr. Garcia - he has offices on Sheldon and somewhere in south Tampa.
To alleviate the problems you could assume it is airborne allergies causing an asthmatic reaction and follow the protocol the doctors would prescribe (minus the drugs and rescue breather).
1. bath every night to get pollens off child
2. put allergy barriers on all bedding (can get them at Bed Bath % Beyond using 20% coupons) - that includes the mattresses!
3. remove all 'soft' toys and upholstery from child's room. If you let them have a stuffed animal wash it weekly with the bed linens which should be washed weekly in HOT water (yes even the comforter!)
4. get a hepa filter for their room
5. eliminate carpet or use dust mite powder on the carpet once every 6 months
6. never allow pets in the bedroom.
7. never ride in a car with the windows open if the child is in the car
I'm sure there were more, but those were the highlights I remembered. It will cover the major common allergens - pollens, dust mites, pet dander - mold is always an issue so keeping your a/c on was also recommended.
Good luck