L.S.
More than likely, and if his sinuses are draining down the back of his throat, like post nasal drip, he could be accumulating phlegm in his tummy and it is making him queesy. Try n all natural saline spray or nasal drops to clean his pour little nostrils out, maybe give him a little relief.
I know that everyone first reaction to a cough is cough medicine, but cough suppresants can actually do more harm then good in most cases... look for something more like an expectorant to help him bring up the stuff that is running down his throat.
Keep an eye out for aspiration and fever, if he seems like he has inhaled some of the stuff and starts a fever, you might want to call the doc so he can rule out aspiration pnuemonia.
I am sure it is just the little bug that is going around and he will be back to his normal self in no time! Best wishes for a speedy recovery for the little man!