Hello, I'm Dr Gary. I saw that you requested a second opinion.
I would have to agree with Dr Peter that x-rays are the next step if they have not been done. Even if they have been done and it's been more than a month- I would repeat them. Many times we can see changes if we have serial x-rays.
If the x-rays are normal, then we rule out things like heart disease, bronchitis, pneumonia, collapsing trachea, masses in the lungs. What we don't rule out, is a mild inflammatory airway disease or lungworms. For those conditions, the best option is a tracheal wash. That is where saline is flushed down the trachea and into the lungs, then sucked back up into a syringe. That fluid is evaluated under the microscope and also cultured for infectious organisms.
If this is an allergic condition, we treat with steroids (Prednisone orally or Flovent through an inhaler) and often times a broncho-dilator (Albuterol inhaler). If it's lungworms, we treat with an anti-parasitic.
I would ask your vet if they are comfortable doing a tracheal wash. Many vets can do it, but others will refer out to a specialist to perform this.
I hope this helps, let me know if you have any other questions.