I went through something similar over decades with my migraines. "I don't believe you're in pain. Men don't get migraines." I heard, far too often.
This is not medical advice, but just what I would do in a similar situation.
I'd go in knowing I'm going to have to keep at this constantly until I'm on a treatment regimen that handled it well, for starters.
I can usually have mixed results speeding things up saying I'm ready to pay right now with a card for whatever medication/test. If someone's unavailable for scheduling then call around to every other place. Call out of the area if needed. Like you would call around for a dentist if you needed a root canal or crown asap.
Edit-Oh, also, the best time to call providers is 7-8 am on Monday or when ever they first open on their first day of the week. The worst time is anytime else, with within an hour of closing being a far maybe. But be persistent regardless, and especially if start of business Monday is too far away.
For back pain I'll try to outline some options for relief in the meantime:
-Try this shortly (20 minutes) and see whether it feels better/worse: Get something that does "far infrared" heat and try it on your neck/spine. You want to be careful to not overdo it on the heat though so use a towel between you and the heat and look for redness. Redness should be avoided. A low-cost/immediate way to try out far infrared are the instant hot packs sold at corner stores like Walgreens/CVS. Try to get the ones that are made with iron. They're basically a slow exothermic reaction that can last 8 hours+.
-Cold might work if hot doesn't.
-Lidocaine patches ("salonpass"/"icyhot") might help, too. Again, try temporarily (10-20 minutes) and see how you react to it. There are even sprays or gels (think, for sunburn) that can help locally fend off pain a little.
-A TENS unit has helped with muscle spasm pain for me before, too, but I had to leave it on the area for about an hour. Edit-look at some anatomy pictures for what muscles to target.
-A physical therapist might actually be able to help you. Look for good ones that are obviously kept up to date on things. I had one mixing ultra sound and TENS on my back and it helped immensely. The TENS made it so I could feel the ultrasound vibrations. You want to go to them to make sure you're doing stretches with proper form. X-Rays and such will help them know what to target.
Good luck, chronic pain in America is both common and not always treated equally.