The best thing to do (and most effective) is to place him in a steam-filled room (like a bathroom with a running hot shower or really hot bath), close the door and stay with him for 15 to 30 min. The other thing would be one of those cold mist vaporizers.
Don't know if you have a health food store anywhere close. Mullein leaf helps really well. You can get it in a dropper bottle. Put 3 drops on a teaspoon with water and give it 3 times per day.
You can get Vitamin C and give 500 g 3 times per day.
If you can't find the mullein leave tincture, you can get one of those herbal cogh syrups at the health food store. It should contain either of the following wild cherry bark, licorice, comfrey root, colts foot, mullein, slippery elom or horehound.
Do NOT give him baby cold medicine! Most of them contain ingredients that dogs cannot metabolize, especially Tylenol or ibuprofen. Aspirin is okay for dogs for pain.
I know you are worried, just let him rest, give him the cough medicine stuff and let it run its course. It is probably a little more uncomfortable for him because of his short nose, you can do the steam "bath" a couple of times a day.
I know how you feel, by now I have 4 dogs hacking away and 1 sneezing and sniffling.
Some naturopathic doctors recommend to put the dogs on a liquid fast at the onset for 2 to 3 days. I am not doing it with my dogs, I think they'd be eating my sofa and curtains
Hang in there, he'll be better soon.