I suggest going to HR in person. When I was looking, one place had me fill out a long application but never got back to me. But another immediately called up a nurse manager who came right down, showed me around and gave an informal interview.
Where there is a demand for nurses, many facilities are inundated with applications and may not have the staff to adequately follow up with each application. They probably just accept that many people are applying to several jobs and if HR hasn't been able to get back to them within a few weeks, perhaps they don't even bother following up, assuming that those applicants have probably taken jobs elsewhere.
Another approach is to try to contact floor nurse managers directly. Some might find that too aggressive but to others it will show your willingness to go the extra mile. If this sounds too forward, ask working friends to ask their manager if you can contact them. Having a strong, willing applicant come to them can save them some effort. Even if they're not hiring right then, they can probably give you useful feedback in your job search
. And if an opening comes up, they might remember you!
Finally, persistence can sometimes work, too. Regularly call or drop by the HR department - or periodically contact a nurse manager - of a place you really want to work. If you're clearly willing and ready to take up a job offer week after week, you will likely be a first pick when selections occur.
Often, it's just a matter of timing and it sounds like these last few weeks haven't been the right time. It's okay if it takes several months to land that first job. Hopefully, you'll be staying there for awhile, and in the big picture, a few months is worth waiting for a good job.