Coughing and sneezing noises can indicate serious respiratory, cardiac, or metabolic disease or they could be something much less harmful such as reverse sneezes.  A reverse sneeze itself is not harmful and is seen more often in short-nosed dogs and beagles.  Many owners become concerned when they hear a reverse sneeze and may think they have an emergency on their hands, but a reverse sneezing episode will only last a few minutes, at most.

While the best thing to do is let your veterinarian see your pet in order to do a full evaluation and rule out diseases or conditions that can harm your pet, comparing your pets activities to these videos may help you discern between a reverse sneeze and something more serious:

Reverse sneezing video