This is too bad. Prior to this person saying anything to you, you enjoyed your job and had no problems? I say, if you like it, stay.
What she said is only heresay.
If you ask me, this person has no class whatsoever. She should never be in management, b/c she can't keep her bigmouth shut. Yet, she suggests you say something about what you heard? have you considered she is trying to set you up? Maybe she is jealous b/c the docs DID like you? Then if you say something, and you tell them where you heard it, why wouldn't she be concerned that she would get into trouble? I'll tell you why, she has NO intention of admitting she shared this info with you OR backing you up!!
If someone wants to tryly help you or be your "friend" in the workplace, they will jump in when you are drowning and throw you a lifeline. Not this way, but when your pt is coding, they will watch your other pt's for you and take vitals w/o having to be asked. They will answer your pt's call lights if you are tied up with a grieving family. And, when they have a problem, you do the same for them.
This "nurse" is NOT helping you by telling you this. Furthermore, it wasn't even said at work in any kind of formal review? This is crap!
I would possibly just ask the nurse manager, in private, if there have been any complaints about you. Do not offer any more than that. Just say, I would rather not disclose where I heard this from, but if there are any problems with my performance, I would like to know, so I can correct them.
Do NOT stoop to her tattle tale level. You only need to be concerned with yourself and your performance. Your "friend" does not seem to understand this concept.
I would be the first one to tell you to leave a job if you were given unsafe assignments, or really getting verabl abuse, but you did not mention any of that, and if it weren't for this person, you would otherwise have had no problem with your position and seemed to enjoy it. (?)
If however, you feel so betrayed that you can't go on in this place, considering less money and travel, just be aware, that people like this exist everywhere. She is a snake and an agitater. It could even be worse where you go.
My advise? Don't do anything for a few days, think on it, go out and watch the sunset by yourself. Make a list of pros and cons to staying or leaving. Don't let someone else burst your bubble. As far as I can "read" this situation, you are being fed BS by this person. Don't let her win, unless moving on is what YOU want.