This sounds like Tracheal problems such as irritation or a collapse which is very common in both poodles and Shi Tsu, though Poodles suffer from it more often.
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. 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. 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 as it often ends in gagging. 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.
Steroids are the most common form of medications used. They are very effective and typically they cause no other problems with the dog. You may want to try daily steroids. There are other medications, the fact is steroids tend to work best for it. There are others as well such as cough syrups, which help mask the symptoms and give some relief but are not good as a long term treatment, antibiotics if a infection caused the collapse. Cough suppressants such as Hydrocodone or Torbutrol may be handy for sudden attacks and have no draw backs. Corticosteroids such as prednisone are also used as short term treatments as they typically cause problems with the liver and kidneys. Airway Dilators such as theophylline or terbutaline are controversial but are sometimes used when surgery is not a option.
I can not recommend one treatment....because I can not exam the dog and tell you how bad the situation is. The dog will need to be examined and the tracheal xrayed to determine how bad it is and which is the best treatment.