Does this seem like a good path to be a physician?

I’m going to go school at a Community College for 2 years and try to get into Nursing school which is about another 2 years. The Nursing school that I am going to offers a contract; if you work for them for 2 years after you finish nursing school, tuition will be free. During the 2 years I work I want to take the remaining Pre-reqs required for med school (Bio 1&2, Physics 1&2, Organic 1&2) then I’m gonna apply for Med School.