Its not too late to apply for a job that starts in May. Work for a year and reapply this fall with a better app.
Most people apply for jobs in a hospital, but without a medical or nursing degree the best job you can get is a paper pusher, something that has nothing to do with patient care and won't give you any real medical experience to put on your resume.
I went the other route and applied for research jobs. Apply for Research Tech positions at local med schools that do research. A Research Tech pretty much does the same thing you did in Undergraduate Research (I'm assuming you did that or knows someone who did...). So the work is pretty interesting and challenging. Pays like 30k a year by me to.
It's not something you want to do as a career, but its not bad at all to work for a year in research and take evening classes to boost your GPA.
You get biomedical research experience, you get a better GPA, you make $30,000, and you get some powerful PhD's to write letters of recommendation for next year. Not all that bad really