You're speaking with Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply.
I'm sorry to hear of this with Nanuck, Sharon. Coughing that develops shortly after being intubated for anesthesia is usually due to tracheal inflammation from the intratracheal tube whose cuff may have been over-inflated or the tube traumatized the trachea when inserted or removed. This type of cough usually abates within a few days unless the inflammation becomes secondarily infected. Coughing that develops within 3-10 days of being hospitalized is usually due to infectious tracheobronchitis contracted while hospitalized (a nosocomial infection). This type of cough should abate within 1-3 weeks of the onset of signs even untreated.
I see that the oncologist reviewed the films and found no evidence of metastasis but did the oncologist comment on other changes in the chest such as increased brochovascular markings indicative of a infectious or sterile bronchitis? Did Nanuck's heart and trachea appear normal in the X-rays?
When X-rays don't reveal the source of such a cough, more invasive diagnostics are considered such as a tracheal/bronchial wash which allows us to examine the cells in the respiratory tract and to culture the wash looking for specific infectious agents we might treat. Scoping of the respiratory tract might be needed as well. Which medications have been prescribed to Nanuck, please?