There are lots of positions in a hospital besides janitorial ones, jobs that pay a lot more than $10/hour.
Hospitals are usually good in terms of offering their employees education perks. Even if you take some courses in time management, etc. it could lead to opportunities in the department you are in now. Every subordinate needs a supervisor, every supervisor has a manager, etc. People in those positions move on to other opportunities, opening up their positions to senior staff among the team. Find out what is needed to qualify for a supervisory position or a management position. There's nothing wrong with being part of the custodial / housekeeping team of a hospital. They have an essential and vital role in infection control, but also in making a patient's hospital stay comfortable.
I've been a nurse for over a decade, and while some of my colleagues keep their distance from the housekeeping staff, I know all the names of the housekeeping staff in my area and chat with them when there's time, and have gotten to know them beyond their name-tags - it makes a world of difference to build that kind of relationship, because these folks will go out of their way - above and beyond - for you if you've invested the energy into including them as part of your team. The patients love it, the housekeeping staff enjoy the praise and gratitude, and my aloof colleagues are bewildered that the housekeepers will bend over backwards for Nurse Scully.