Do they not have flu clinics in your area?
From the sounds of it you need to pay for your flu shot, but in my area, even back when most people had to pay for it, there were still flu clinics. The public health agency would rent space from a mall, or rent a community hall, or something similar. They'd post ads about the flu shot clinic being at a particular place on a particular date, and then the hours that the shots were available. Then it was first-come, first-served. We still have that now. You can get your flu shot from your provider or from a pharmacy, but the flu clinics are very popular. That's often where I get mine.