All of the above have good suggestions; I would definately take this to the powers that be, as this person sounds like she is slandering your good name/repitition and it could hurt you in the long run. Misery loves company, so if you try to move to another department or even hospital for that matter, this could follow you. Hearsay can be extremely dangerous, rather true or not. If nothing is done, I like the idea of an attorney, protect yourself or at least talk to an attorney if it comes to that. Continue to do your job, sounds like your doing it well, ignore that person; SHES IGNORANT, don't give her the satisfaction of her knowing that she's getting to you, all the while, documenting everything that shes doing; in the end, people will see her for who/what she really is. Keep up the good work, pray if you have to, to get you through the day, but don't give her anymore ammunition! Take care honey and keep us posted. Oh do you have family in town, maybe you can be with them.
Also, you really should be careful what you tell people from this day forward, its ashame that its hard to trust people nowadays but until you absolutely know for a fact you can trust someone, refrain from telling your personal business, especially at work. People thrive on knowing other people business! I always say, I go to work to do a job not to make friends, but if I do meet a friend, its a blessing.