OP, I would ask your ortho/neuro (whichever you see) if they think the injury is a workers comp elig injury. Just because it didn't "happen" (I assume you are talking about the onset of the pain) at work does not mean that your disk injury is not a result of repeated heavy lifting from things such as turning, mowing patients up in bed, assisting in transfers, etc. If you are able to get WC you should have more job safety/security where you are now since they shouldn't be able to get rid of you based on your injury/disability alone. Also, I believe that they would be required to provide you with reasonable accommodation, so maybe they would have to find you that desk job if that is what you truly need right now, otherwise maybe they put you on "light duty" with restrictions on how much you are able to lift (maybe have two CNA's do patient repositioning?), a required break every ____ so that you can sit/lay down to relieve pain or pressure on the disc, etc.
I'm sure I will think of more, but I think the big thing here is that currently you are a person with a disability (even if hopefully temporarily) and they are required by FEDERAL LAW to provide reasonable accommodations to persons with a disability, just like they would (hopefully?) try and accommodate a nurse who had restrictions related to pregnancy.
Good luck to you. I see no reason why the hospital you are at cant find SOMETHING for you to do, even if it is helping with DC planning, chart reviews, helping orient new hires..... (If they truly look hard enough they will find a place!). Also, consider seeing an attorney who might be able to go to bat for you if your current employer is unwilling to waiver and insists on breaking the law.