Can I go from a "not-so-competitive" undergrad school to Harvard medical school?

You can absolutely get into Harvard's medical school from a not highly selective undergraduate school. As long as you got good grades during your undergrad years, met the pre-med requirements, and did well on the MCAT, Harvard's med school is as attainable to you as it is to any Ivy League graduate. While going to a big name school can definitely help, what you did during your undergraduate years is far more important. As long as you show that you put forth the effort and took advantages of the opportunities presented to you, Harvard is do-able. I always say that the Ivy Leagues take, above all else, immense dedication and commitment. If you have that, you can do it no matter what your background.