NO! The most important element in getting a remote job is having experience in that job title. Yes, having experience working remotely is nice, but it takes so much less time and cost to train someone how to work remotely than it does to train them how to do the job!
My best advice is to figure out an area you are interested in. Browse job boards for remote positions and once you have identified some jobs you might like, apply to those (DUH!), but then also search for those same positions in your hospital or local area. If you can get 2-3 years of solid experience in that job position, it will be so much easier to find a remote position later.
I would definitely apply to anything you are qualified (or mostly qualified) for, but getting some solid experience in that job role will seriously help!