There are many non-clinical volunteer opportuities to demonstrate that you are willing to freely give your time to improve your community (community being people in your area) including literacy volunteers, mentoring/tutoring kids and teens who don't have adult role models in their lives, teaching science/health class modules in under-performing schools, friendly visitor to the elderly, providing musical entertainment to nursing home residents, coaching kids and teens, organizing blood drives and/or bone marrow registries, providing disaster relief services (tornado, hurricaine, flood, etc), home construction projects for the poor, food pantries, soup kitchens, staffing an overnight homeless shelter.
You also need some exposure to medicine/health care. Most people think hospital volunteering is a "two birds, one stone" situtation but you could be employed in a health care setting or in pre-hospital care (EMT), or just do shadowing and get that exposure to medicine/health care/sick people.