what do you think;to get to your car after work and fall on your back ; Work comp or should your Auto Pay?

Workers compensation may be liable if you promptly notified your employer of the injury. The drive to and from work is not covered by workers compensation, but in some states the walk to and from your vehicle is considered part of your job and is covered by workers compensation insurance. A quick call to a local workers comp attorney should let you know if this is compensable by workers compensation or not.

There's definitely no reason that your auto insurance has any liability on this matter.

If you were "off the clock" then there isn't anything you can do, generally speaking. It would help to know what state you are in. Some states DO cover you when you are on work property, but those are few & far between. I suggest instead that you try to work with your employer to take on "light duty" or another job. Also, your physician can help you in this area. Your employer must also display workers compensation information AND make it readily available upon request. Go ask for it.

Because it happened on your employer's property, you might be able to get worker's compensation. It might be difficult though because you were off the clock and leaving work. Usually employers aren't automatically liable for employee's injuries if they are going to or coming home from work but because you were on their property, there still might be some liability.

I don't see how auto insurance would cover it if it has nothing to do with your car.

Did you have an auto accident? Then no, your auto ins would not pay.

Workers comp may, depending on your states (which you did not provide) laws. You can also simply sue the employer.

You did not provide enough facts on what caused you to fall to make an educated answer. Simply because you fell doesn't make it anyones fault but your own. Believe it or not, you can actually hurt yourself without it being someone elses fault. Its called personal responsibility. You fall, its your fault and you move on. But, everyone sues today because nothing could possibly be anyone elses fault.

So, unless the employer did not clear snow or ice or have badly maintained walkways...how is your falling anyones fault but your own?

I would think health insurance. Not sure, though.