Consulting right out of undergrad with research exp. Please advise!

Rank: Monkey | 58

I am a recent graduate from a non-ivy/target school (GPA: 3.9+) with work experience in a biomedical research setting. Just published a first author paper in a great journal this fall. My career goal is to become a physician but I've been in research for a few years now and would like to gain other skills before starting med school in two years.
Being that I am from a public school (very few from my school have gone into consulting etc), I have had no luck in getting my resume noticed thru online applications. I also have NGO internship experiences but Im not sure how relevant that is.
Any advice for successfully applying? Thanks

Also, does reaching out to random recruiters on linkedin actually work?