What are my chances, and what can I do to improve my chances of getting into Med School?

I’m graduating next year from a top 20 public university with an undergraduate degree in nursing. However, my goal is to go to medical school. It’s looking like my GPA is going to be between 3.8 and 3.9 by the time I graduate based on current GPA and number of credit hours left. Preferably, I would like to attend an Ivy League medical school because I enjoy research as well as hands on medicine. I plan on working for 2 years as a nurse before going to med school so I can get some experience. Currently, I volunteer with an advocacy center and assist victims who have experienced sexual assault. How likely is it that I would be accepted into a med school like Harvard or John’s Hopkins, and what else can I do to make myself stand out as an applicant?