Volunteering at the nursing home and tutoring kids may not be enough. (I personally don’t think they are, for a stem wannabe to a competitive holistic.) What do you actually do at the hospital? Research (especially when facilitated by the hs) doesn’t replace the hands on aspects. Are their more ECs than sports? Nothing collaborative in math or science? Nothing that shows other interests and openness? Or challenge? You need to quickly take a hard look at what your targets expect in a stem wannabe. A bsmd program will be even more competitive.
No, you don’t need a top undergrad program. You do need a school where you can do your personal best. So right now I don’t think you know enough about either UG acceptance or what it does take to get into med school. Try to learn more.