Ummmm.... why not take him to the vet to bet sure it's nothing to worry about?
Yes they get colds. From your description it sounds like the dog may have bordatella, otherwise known as kennel cough. They don't have to be in a kennel or close quarters to get it, they can pick it up from another dog they meet just like we can pick up a cold. If it lasts more than a few weeks or he seems to be losing too much weight or super sick then I'd take him to a vet. I think it usually lasts 10-14 days or so, but the coughing can linger a while just like in humans. Many people describe kennel cough as sounding like a deep hacking cough.... which may be what you are witnessing when you say he's "trying to be sick."