need advice

Unless future employer brings up the subject I'd forget it. If they do ask tell the truth.

There is no reason why you have to tell anyone "I left one week after handing in my notice." The only reason it may come up is if your prospective employer is told this by the NM and asks you about it, but unless you've given written permission for your NM to answer all questions about you, this won't happen.

Someone is going to come on here and tell you that employers are not allowed to discuss anything except dates of hire and resignation, but that's not entirely true. Prospective employers are now getting around that by having the candidate sign a consent form allowing the previous employers to answer specific questions, such as "Eligible for rehire?", etc. Don't let this scare you, if it comes up explain what happened. It sounds like you had a legit reason for doing what you did, and I think a prospective employer would see that...especially if you're stating facts and not pointing fingers.

I'm a new member here. In my "other life" before becoming an LPN, I worked in Human Resources as a Recruiter for many years. I never asked a potential employee if they worked out their notice period at their prior job. The company's policy was to do telephone verification of prior employment. I would ask the former employer if the potential new hire was eligible for rehire, and if not ask the reason why. But, no reason for you to disclose. I doubt it will come up, but in the event it does, just be honest and factual. I had a similar situation happen to me once. I won't go into the details, but I left a job (not nursing, in Human Resources) with no notice. I was asked to do something that compromised my ethics. I chose to leave. I did not disclose to future employers that I left with no notice. I never experienced a problem. Best of luck to you!!!!!