A common cause of the symptoms you are describing is a collasping trachea. The condition resulting in a weakness of even a genetic defect of the cartlidge rings that comprise the trachea. A Vet would have to confirm using a scope to look at the trachea.

Other possibilities contributing to gagging/chronic cough are:

1. Migration of round worms from the lungs to the stomach completing their life cycle.

2. Stomach reflux irritating the esophagus triggers a reflex. Acid blockers resolve the problem.

3. In older dogs - possible heart problems.

In another words it's an arm and a leg time for you. If the Vet says everything is fine, then ask them about the possibilities listed above.