Just like CapeCodDreamer said, you can work in rehab,dialysis centers,pediatrics,veterans facilities, and home care..There are places that will hire you without experience, but some may require exp in a hospital like setting so I suggest getting your feet wet and just start off working in a nursing home for the experience then transfer over into one of those sectors. Put in as many resumes/apps as you can,something is bound to pop up for you! Keep us posted with what you find in your state..
look up patient care tech or patient care services,this position is usually in a hospital setting and has on the job training. Could be titled differently in your state.