This is not a criminal law question and not a violent crime. If anything, there are questions of malpractice. I am not an expert an malpractice but I think you would not have a case. Even if you did, I doubt you'll be able to find someone to take the case.
I do not believe there is a viable claim here and I believe you would have difficulty finding counsel.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
There is certainly no crime described in your question. It sounds like you want to accuse them of medical malpractice of some sort. In Arizona, you have to find an expert in the field willing to render an opinion that there was malpractice before you can file a claim. Just because a nurse was incorrect about the onset of labor, and the fact that you and your "prego girlfriend" are irritated and inconvenienced, does not give rise to malpractice, nor criminal liability, nor tort liability.
What if she really was in labor, but the hospital failed to do the necessary procedures to find out? That would have certainly been malpractice, and I suspect that you would be eager to sue them for it, as that would be your right. The fact of the matter is, nurses and doctors are trained to check things out and take certain precautions. Just because she was arguing with the nurse does not relieve the nurse of his duties. It only makes performing those duties more difficult and unnecessarily tiresome.
I recommend trying to cooperate and work with medical personnel as much as possible, rather than waging petty battles with them. The beneficiaries of your cooperation will be your child, your child's mother, and ultimately, yourself.
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The basics of what you described do not rise to the level of medical malpractice. The hospital personnel may have been overzealous, but it does not sound negligent.
I cannot comment on the potential criminal aspects of the events, but believe your girlfriend would be better off filing a written complaint with the hospital's risk management department. She will likely receive, at most, a phone call with an apology.
This answer should be used for informational purposes only. It does not create an attorney-client relationship with any reader and should not be construed as legal advice.