What you are describing sounds like it may be a reverse sneeze instead of collapsing trachea.
Check these videos out to see what you think:
Reverse Sneeze
Collapsing Trachea:
It very well could be CT, but thought you should see the difference between the two. With reverse sneeze they breathe in and out rapidly making snorting sounds. With CT, it is more on expiration and is a honking sound that they make.