MD Late comer to the game!

I've just transferred to NYU as a Junior and I have just started my pre-med requirements. I was advised to wait until I transferred into my 4-year institution to take my pre-med courses so that they held a higher stature on my application. I'm really really nervous about doing well and I would like some tips about how to get into the game so late.

Just some background, my father is a pediatrician who is very supportive but his advice is a bit outdated (by 40+ years). I transferred with a 3.89 GPA and have only taken Anatomy and Physiology courses and several math courses that don't apply for medical school admissions. I haven't had a lot of volunteering experience but I have had a lot of work experience teaching dance, gymnastics, and cheerleading (does this show leadership and trust?) and working administrative jobs. I don't have much time left until I am no longer eligible for undergraduate student loans so I have to find the best way to manage my time.

I've just moved across the country from California so I don't know any hospitals or doctors in New York City that I could shadow or even where to start with volunteering. Any and all advice is gladly accepted. Also, if you live in the New York City area, I would be very interested in bribing you with coffee to pick your brain. :)