Depends more on the doctor and the reason for a visit than simply being in North America. I can see my family practitioner same day/next day if I’m sick. Otherwise I might have to wait a few days. The only doctors my family has ever had to wait three or four weeks for appointment are those that book follow-ups months out- for example, my husband has sleep apnea and sees the sleep specialist every six months. When he saw the doctor in December, he made an appointment for June. Husband forgot about that appointment and missed it. When he realized in August that he missed it, he was given a new appointment four weeks away- because most of the August appointments had been given six months earlier. They apparently leave some slots open for new patients, because there wan’t a wait for the initial appointments.
You need to face facts and accept that she’s just not into you, dude.
Go to a walk in clinic. Then when you are sure there is no immediate danger you can book an appointment with your regular doc.