My dad is technically still a nurse, so uhm, yeah I know a thing or two. In Europe at least, most admin positions are filled by people with degrees. You will need a degree to be promoted to an admin role. In fact, there are even degrees in nursing these days, which give preferential access to stable roles in areas where offer outstrips demand (i.e. poorer regions).

The best you can get without a degree is leading your own team of nurses, which basically means deciding shift patterns. My dad sorta invented his own job (back in the '70s when the world was more flexible, let's say) and "escaped", but most people he knew are still there doing shifts.