I recently helped a neighbor with his broken spring mechanism (old 60s house in San Francisco). The whole thing was made out grossly inadequate metal which had sheared. What started out as a simple welding project turned into substantial reengineering just to get the door to work to get his car out.
Final lesson: steel fatigues and cracks from work hardening and bad tolerance installation. If you have an old door mechanism, don't trust it. Replace it. They're moderately expensive, but the modern ones are not nearly as hanky as the older ones. Don't DIY a garage door unless you have good levels of hands on fabrication experience and a good practical knowledge of what type of fasteners to use to anchor the door hardware to the building substrate. (I.e. Deck screws won't work.)
Very very scary stuff, large springs. Even small ones are not without danger (think old alarm clock springs, those can take an eye out when they let go).
Best of luck with your recovery, I really hope you get back to 100% functionality. And thank you for sharing the story, it just might help save someone else from doing something like this.
edit: more risky springs are found in the suspension of vehicles, don't mess with them without the right tools and knowing what you are doing.