Both times my son had vomiting with his cold/cough, he had pneumonia. He would also have a relatively low fever that would come and go too. It would be like 100 in the morning, then it would go away for a day, then the next day it would be 100.5, etc. We had to take him to urgent care to get the diagnosis both times.
If this is continuing, and if he has been running a low fever on and off especially, I would insist that your doctor give him a chest x-ray or take him to urgent care where they are generally so thorough that if you tell them your son has a cold and is vomiting, they will automatically do a chest x-ray. I don't want to scare you, it may be a totally benign cold but it's worth checking out.
Hope it all goes well!