Nursing is in many ways a funny world. We do have some of the attributes of a profession - like a high level of skill and knowledge and a strong professional duty to put the interest of the patient first. But other aspects of being a profession - like setting our own standards of practice and our own rates of compensation - elude us unless we act in unison with other nurses.
I'm not willing to let some bean counter tell me what my standards should be. And I live in a community where I am deeply rooted and where there is only one hospital. So, for me, the only option for protecting my wages, benefits and standards of practice is to do it in concert with other nurses - in other words, a union.
Those who say you have legal protections are maybe sort of half right. There is no legal protection in most places against unfair termination. You can't be fired because of
your age, or your race, or your gender, but you certainly can be fired for no reason at all. You are an "at will" employee and your employer can fire you just because they are tired of seeing your face or because you mouth off too much or whatever.
It is illegal to fire you for trying to organize a union, but that law is routinely ignored. The penalties are so light and the enforcement so poor that the employers
have no incentive to obey the law. The absolute most that can happen if you are able to prove you were fired for that reason is you get your job back. No damages, no penalties for them.
It is true that "right to work" just means that union membership is optional in that state. But in practice, states with those laws also tend to have very poor legal protections for workers, poor workplace safety laws, etc. Good laws in those subjects get passed because unions push them through the legislature. No unions in a state means weak legal protections for workers too. And there can be a huge gap between what the law says and how it is enforced. In your state, for example you have a governor who doesn't believe workers should have ANY rights, so the person appointed to head the agency that enforces wage and hour laws was appointed by that governor and probably doesn't think so either. So, yes, there may be some rules requiring them to give you a break, but highly unlikely that you can get it enforced effectively by yourself and likely you'll be fired if you try.
Organizing your own union is next to impossible. Too much to learn and too many ways the hospital can block it. Unions are beginning to come to the south, but it's a slow process. And it tends to be strategic. It doesn't make sense to just randomly organize single hospitals far from a union's base, so they tend to look for opportunities to organize several in an area. NNU (National Nurses United) is branching out a lot. In the last 18 months or less we have won 14 organizing elections in Florida, with another one coming up soon. So the day when there are real opportunities to organize in other southern states may not be that far away. Your options right now are pretty much be patient or move somewhere else.