Re: American interested in Nursing
Key question: What languages do you speak?
Yes, there is a need for nurses, but of the maybe dozen or so US qualified RNs I know living here only four have found nursing jobs. The others have not yet reached the proficiency in German and/ or French, Italian needed.
All came here as dependents of their (headhunted) spouses or are married to Swiss/EU citizens so the residency permit wasn't the initial stumbling block that it would be for you if you are trying to move here on your own. The stumbling block has been language proficiency to get their qualifications recognized, and then demonstrating the level of 'on the ward' fluency needed to be hired.
A few of the nurses I know have given up, as they felt that in the time it has taken to reach German proficiency they have been out of the field long enough that their skills are no longer up to date. Shame, as they were highly trained in specialized fields, actually educated far beyond the typical Swiss level for nurses.
One who is working was an NP in the U.S., but this profession really does not exist here. She is frustrated at having lost the ability to practice at that level, but at least she has a job.
One who is not yet fluent enough to work as a nurse has found a job as a care assistant in a nursing home, a far cry from her training, but again, at least a job. This kind of job would likely not get you a work permit, though.
TL;DR: Yes, there is a need for nurses. But if you don't yet speak German (French, Italian), learning to do so should be a priority.