If you luck out, and depending on how you're able to spin your prior exposure to healthcare, you may be able to find a medical assistant job that doesn't require certification/experience and will train you on the job. They're not easy to find, but they are out there.
Becoming a CNA requires very little education -- you can get certified in as little as a month -- and there are often similar "caregiver" jobs that will take people with no training. Some hospitals and nursing homes have programs that will provide you with free CNA training and certification if you commit to working there for a certain amount of time afterward.