This sounds like Tracheal problems such as irritation or a collapse. Likely brought on by the sneezing.
Tracheal collapse is a condition in which the trachea partially collapses as a dog breathes, leading to tracheal irritation, coughing and sometimes secondary changes in the lungs or upper airways. It is most common in toy breed dogs but can occur in larger breeds at times. It is reported to be most common in Terriers, poodles, Chihuahuas, pugs and Pomeranian have been reported to be the breeds most commonly affected by this condition but it is reasonably common in all the toy breeds and several other smaller dog breeds.
The irritation is self perpetuating, since coughing and increased respiratory efforts lead to further irritation and worsening of clinical signs. Eventually, damage can occur to the lungs, larynx or even upper airways. Obesity, irritants, allergies, concurrent heart failure, bacteria, viruses can all contribute to the problem, as well. If a pet owner smokes.
Smoking by the owners does seem to be a factor in initiating and prolonging symptoms of tracheal collapse. The symptoms of tracheal collapse are coughing, difficulty breathing and tiring easily. When this condition first occurs many dog owners truly believe that there must be something caught in their dog's airway due to the severity of the cough. If the tracheal collapse is occurring inside the chest the increase in pressure on the circulation can lead to heart enlargement or contribute to heart failure.
There are medical treatments for collapsing trachea as well as surgical treatments. The consensus of opinion seems to be that collapsing tracheal problems are best treated medically until it becomes obvious that medical treatment alone is not going to work.
I would suggest taking him into see his vet today and have him looked at. If this is the cause they can start him on some medications to ease his discomfort.