Are you supposed to call and make an appointment at an auto repair shop?

Many places yes you should call ahead of time. I'm sure you could always just go in but they might not be able to see you that day if they are busy.

I had an appointment to bring my car in to get fixed today but they ended up sending me to a different repair shop that could do the job better. I just walked in there and had to wait about an hour before they could see the car, but I had no appointment there.

If you are in limited time better to call ahead of time.

It is recommended.

If a shop is not very busy, they may still take you in but they will work on the cars that already have an appointment first in order to get the vehicles back to the customers and then work on your vehicle as time allows.

Yes. They are normally booked up so you would need to make an appointment.