Employment Law Questions? Ask an Employment Lawyer.
Is this a private hospital or a hospital owned by a government (city or state)?
Did you work under a written employment contract or a union contract?
Did any employee manual, hospital rule/policy, etc. indicate employees could only be fired for certain reasons?
Was there a set policy to be followed before termination?
What state is this in?
What "confidentialtiy" issues occured?
Normally, unless an employee has a written employment contract or a union contract they are considered employees-at-will (which most Americans are). Employers can hire and fire employees at will at any time, for any reason or for no reason at all, even if they are good employees. However, if a termination decision is due to illegal discrimination then that, of course is illegal or if an employer has indicated that employees will only be fired for specific reasons or that an employee will have a job for a certain time period then there may also be a claim for wrongful termination, but otherwise, most terminations are fine under employee-at-will principles.
As for disclosure of FMLA, if that disclosure may have violated patient HIPAA rights (employers, in most cases, do NOT owe employees HIPAA protections) then that may have been a HIPAA violation. The FMLA does have confidentiality provisions which requires employers to maintain such information as they would medical records (see here).