Hey there,
I am in a similar situation. Currently working in Finance and am looking to apply to a post-bac and pursue medical school. I am going to start applying for volunteering opportunities this Fall (I'm also in NYC) so I can have some experience under my belt. My biggest worry, like you, is that I have no health-related experience, so I am trying to build that up.
From my understanding, the top post-bac programs like to see medical-related experience, but I am not sure how much. I don't know if 6 months of volunteering is enough for these schools (especially if I am applying later this Fall, where it would only have been ~3 months). Given that the rest of my grades, extracurriculars from college, and SAT grades are good, I am not sure how significant of a detractor this would be for my application...any thoughts?