I have been asked to step down from my nursing supervisor role and take a staff nurse position or resign with disciplinary action, can i fight this?

There are a number of issues here and you would be best served consulting with an experienced employment attorney on these matters.  However, if you signed a severance agreement, there may be no legal option for you as that agreement should contain a "release of claims" which will prohibit you from taking legal action.  Even so, you should have an attorney review though the agreement. It will be worth the cost. An employer has no ability to make you resign in North Carolina, but if you refuse to resign you can be subjected to disciplinary action including demotion or termination. Why?  Because this is an employment-at-will state which means you can be fired (or disciplined) at any time for any reson.  You cannot file a legal claim unless you can show there is an unlawful motive behind the decision to demote you.  The facts you post do not show any unlawful motive although perhaps there are other facts that do show an unlawful motive that you have not shared.  Again, something you can discuss with an emploment attorney in a consultation.