Have your vet refer you out to have a flouroscopy done. That will show whether it is CT or not!
http://www.aspca.org/pet-care/dog-ca...cheal-collapse
From the link:
How is tracheal collapse diagnosed?
A honking cough in a toy-breed dog is highly suggestive of collapsing trachea, but a definitive diagnosis may require additional tests. Radiographs may reveal an obviously collapsed trachea, although not always. Fluoroscopy, which allows visualization of the trachea as the dog inhales and exhales, may be necessary to confirm the diagnosis. Fluoroscopy is available only at universities and referral centers.