I hear all sorts of 'horror' stories about people having to wait a long time to get an appointment with their doctor. Usually those stories are about seeing a specialist, and the waits are not because of any insurance issues, but because the specialist has so many patients there's simply a long waiting list to get in.
When I had to make an appointment to see a pain specialist, they needed about two weeks to fit me in. The physical therapist needed a month.
I just called my primary care physician to make a non-urgent appointment. He can see me tomorrow.