It certainly does sound like Canada. I am one of the lucky ones and do have a family doctor and it is still a minimum of 6 weeks for me to book an appointment to see him.
If I am really in trouble, I can go to his clinic as a drop-in (along with dozens of others) and wait, hoping somebody doesn't show for their appointment.
The state of healthcare in Canada is...bad. really bad. Canada's healthcare system is effectively using long wait times as a form of passive rationing, where delays lead to natural attrition of patients. This is a poor solution to address the per-capita physician shortages by decreasing demand rather than increasing access to care.