When we first got Annie, after a few days she got kennel cough. Which I believe is a doggie cold. As this was our first dog, we took her to the vet. It is not necessary to take them to the vet for this. But it has to run its course. It does take a few weeks to get over. If your doggie is coughing a lot you can give him/her a 1/4 teaspoon of cough mixture. When we took her to the vet they gave us some antibiotics to help the process along.
But if you are still worried, it can't hurt to take the doggie to the vet. I know I do