You'll never believe it but it sounds like she is having a reverse sneeze. It's allergy seasons in many parts of the US and dogs are affected, too. With a reverse sneeze, the dog might honk, blow and gasp for air.
Reverse sneezes have the same cause as a regular sneeze but are much more dramatic!
You should look around the home for allergens and eliminate them if you can. Carpet powders, cleaners and pollen are pretty mean culprits.
I found an informative article that might explain it for you better than I can.
Paroxysmal Respiration or "The Reverse Sneeze"
This is a condition very common in brachycephalic breeds and small dogs but is also seen in other breeds. Paroxysmal respiration, which is the medical term or what is commonly known as reverse sneezing is when a dog seems to be sneezing, but in reverse. The episode seems as if the dog is sucking in or honking and it lasts between a few seconds or a few minutes. To us, it appears that the dog is uncomfortable, but it is a common condition in small and brachycephalic breeds and the dogs return to their normal state when the episode is over. Some feel that massaging the neck and throat area help to stop an attack. In the "Textbook of Veterinary Internal Medicine" by Ettinger and Feldman, swallowing will stop reverse sneezing. According to their book, reverse sneezing can also be controlled by massaging the pharyngeal area or by briefly closing the dog's nostrils. Some people say that their dogs respond to rubbing of the upper neck area when experiencing an attack or episode. According to Dr. Mike Richards, DVM "Reverse sneezing is a problem of the pharyngeal region." Though there is no definite known cause of it, some have reported that it occurs with allergies, when dogs become overexcited or overheated, and some experts say that it is common when dogs suffer from tracheal collapse (another condition, common in small and brachycephalic breeds).
I have found evidence that the massage technique mentioned above works well as does forcing the dog to swallow.