I hear a lot of excuses, but not much else.
I had a hernia for 12 years. And, I simply lived with it. But it got to the point that I could not even stand up straight anymore or walk because of the pain.
I moved to California, and a year or so later found the CMS program. Basically, state run insurance for low income residents. I signed up. I went to the "free" clinic, which referred me to the surgeon, which scheduled with the hospital - and it was taken care of at no cost to me. All within a month or so.
In the end I had 3 hernia operations. Complications with the first, and a second on the other side were the other two. But all were taken care of quickly - and at zero cost to me.
So, try to get treatment with no insurance? It is very possible. Even likely.
And if you have a broken neck, I would say that you would fare as well or better. So stop with the crying and get yourself fixed! Most states have these types of insurance programs. And if they don't, no ER would turn you away.
Going into the military with the hopes of getting this fixed is very dangerous. If you start boot you may end up dead within a few days because of the physical requirements. And if you get in and immediately try to get it fixed, you would probably be kicked out with a dishonorable discharge for lying about your medical condition.