Wow, I'm so sorry you had such a horrible experience during your sleep study. What they attempted to do was a split study, which is first test you without CPAP, then test you with CPAP and the mask. But since you didn't complete the second part, called the titration study, they want you to have that on another night.
If I were you, I'd ask either the sleep study clinic or the doctor for a copy of the sleep study results. The doctor ought to go over those results with you, but it's good to keep a copy.
It's not uncommon for them to order you a CPAP machine before you have the titration (sleep study with CPAP), BUT that machine should be an auto CPAP. In fact, it's not absolutely imperative that you have the second sleep study. They can evaluate the effecacy data from the machine (if it's an auto CPAP). But keep in mind, even with having the machine first, it may still be necessary to have the titration, especially if you're having any problems breathing with the machine. You may need a different kind of machine, and that is typically determined during the titration (but not always).
But I was like you. I was shocked to learn I slept enough for them to determine that I had severe sleep apnea. But I had a sleep doctor who showed me the results of my sleep study, showed me the graphs and the numbers that showed how many times I stopped breathing, and what my blood oxygen levels were. That made it easier accepting the CPAP machine.
Not everyone tested has sleep apnea. But often there is enough reason to suspect there is sleep apnea (based on patient comments and maybe blood oxygen levels), so that it's logical that most tested do have sleep apnea.
Are you sure the hospital is the only place to get CPAP equipment? You might call your insurance company and ask what suppliers in your area can provide you with a machine, depending on your insurance (assuming you have insurance, if you don't, then maybe there are some other medical supply places near you or not far away).
Whatever you do, insist that the doctor order you a machine that records effecacy data, and preferably an auto CPAP machine if possible. By effecacy I mean the machine records more data than just compliance (when you use it), but also AHI (apnea hypopnea index, how many times you stop breathing while using the machine), plus mask leaks and more. Auto CPAP machines typically record that. But some straight CPAP machines only record compliance. Make sure your doctor orders effecacy with the machine. They know what that term means. It's a diagnostic tool that all patients should have. Some doctors will only order the basic machine that records only compliance.
My sleep study was horrible too, but not as bad as yours, I think. At least the bed was better!
Let us know what happens.