Hi, HockeyDad
Three cheers for your third doctor! My husband's primary tumor did not show up on the CT scan either, but did on the PET - so that should give you better information.  As others have said, make sure they do the evaluation for 
HPV. 
It is very important that you are evaluated and treated by a team that is very familiar with oral cancer. A tumor board (consisting of ENTs, ROs (radiologists), MOs (medical oncologists) and possibly SOs (surgical oncologists) should jointly decide on your course of treatment - not a single doctor. An official Comprehensive Cancer Center probably offers the best environment, but my husband was successfully treated at a public hospital by a team of excellent physicians. 
Best wishes and keep us updated.
Maria