I'm so glad you got approved on your first try!
As for your health insurance..I SO wish you would have asked that question immediately upon being laid off! What you NEEDED to do then was to apply for and get COBRA...a sort of "bridge" health insurance between the job you left and a new job..even though in fact you weren't applying for a new job. I don't think you will be eligible anymore..and it is very expensive, so you might not be able to afford it anyway. But it wouldn't hurt to check. Start with your state unemployment services and see if they can provide you links to where you can explore possibilities there.
Unfortunatly you won't be eligible for Medicare until you've had SSDI for 2 YEARS. Meaning, essentially, you have no coverage for the next two years. If you can't get COBRA, you won't be eligible for any sort of private health insurance. You might check with your state -- many states have a "high risk" insurance policy available to residents of the state --but again, it's very expensive.
Other than that..about all you can do is negotiate with your doctors..let them know you have NO health insurance until the Medicare starts, and see if they will provide you with care at a reduced price. A tough spot to be in, for sure.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....