If what was stated in the complaint is absolutely, 100% untrue, you can sue the hospital/facility and name the manager individually in the lawsuit for defamation, slander & libel---what she wrote (and likely stated) to the BON has affected your livelihood, and this is the key point in slander/libel/defamation lawsuits. The hospital would likely deny any liability & throw the nurse under the bus, distancing itself from her actions as much as possible. This is much different than a medical malpractice lawsuit, where a facility's insurance would cover a staff member. A facility's malpractice insurance wouldn't cover a nurse manager's actions as far as defamation, slander & libel--she'd have to hire her own attorney, pay her own legal fees & deal with the consequences of her actions. Even if she had her own malpractice insurance, it wouldn't cover something like this. "Reporters" are not protected by law when they submit a complaint to a licensing board containing untrue claims that defame someone & negatively affect their livelihood, even if they are that person's supervisor/manager. At the very least, you should sue for lost wages, potential lost wages, emotional distress, legal fees/costs and punitive damages for the manager's egregious actions that hurt your career/livelihood. At the very least, she will probably lose her job. And make sure that you notify the media about this---the public needs to be made aware that nurses are being reported by their peers/supervisors/managers with false information, resulting in the nurses losing their jobs, having to pay attorneys to fight the allegations & unnecessary emotional distress. I would also report this manager to the BON for submitting a complaint that included totally false claims & allegations, as honesty & integrity are a requirement of being a licensed nurse. I would be interested to know what that manager put in the complaint about you, and whether the complaint was made before or after you left your job. People that file false complaints, whether they are strangers, superiors, another nurse, your neighbor or ex-spouse, can be sued for making false statements that negatively affect your livelihood, especially to an administrative board.
As far as potential employers finding out about an investigation, as far as I understand, pending investigations/actions with the BON cannot be revealed or published. Only when there is action/discipline against a nurse's license can it be made public.