Cancer, anywhere in the respiratory system, including throat, larynx and lungs can cause a cough, but once begun, it would be very unlikely
for it to continue to diminish.
For that reason, I agree with your primary care provider (PCP) and do not believe a visit to an ENT or a pulmonologist is warranted, unless the cough would recur/worsen in the immediate future.
By convention, a cough is not considered chronic until it lasts more than 3 months.