Will a graduate school of health science accept me if I have no relevant work experience?

I am trying to get into either a graduate entry Nurse-Practitioner or Occupational Therapy program (more likely Nursing), and I've been trying to apply for jobs at places that are relevant to health care (e.g. dietary aide at nursing home/hospital/rehab center, developmental service worker, pharmacy technician, etc.), and nowhere near where I live is hiring for those kinds of jobs. I have applied at all of them and they're either not hiring or won't work with my school schedule, so I'm at the end of my rope and have now been applying at banks and stores, but I'm worried that if I work at a place like that instead of something relative to health care that I won't get into any of the grad school programs I want. Do you think it makes that much of a difference? I'm so worried for my future.