As a preliminary test, you might look at a “sleep apnea adjustable mouthpiece” for sale online. I don’t know how well these work, but my custom sleep apnea dental device has been amazing for me. It may be that the boil-and-bite varieties also work well. If so, you might get relief without having to interact with the healthcare system.

You might find more information here.

As for the sleep test, many factors are important, but you could learn a lot from monitoring your pulse oxygen while you sleep. A casual search turned up several very affordable fingertip pulse oximeters that connect via Bluetooth. This would let you create a record of your pulse oxygen levels while you sleep. If you are dropping below 92% while you sleep (link), then you might be sleeping poorly because of sleep apnea.

In fact, you could record your SPO2 levels with and without the sleep apnea device to rule its use in or out without spending a ton of money on doctors visits and the like.

I hope things get better for you.