If you are really aiming for tip-top schools, then involvement in research will play a much more significant role in your application that at other places, and I would recommend starting earlier than later as research projects take quite a lot of hours to complete (multiple semesters, usually). Shadowing generally has a pretty range of acceptable hours, roughly 50 (better in a primary care setting, imo), and after that it just becomes excessive. Fwiw I shadowed in my junior year for a semester and that worked out fine for me, but ymmv.
I would try to reach out to some research mentors to see what they have available and try to start working in the fall (I actually started in my sophomore fall too, haha). The first semester of work is generally just getting you used to the techniques and analyses rather than independent project (especially bench-top research), so it shouldn't be too much of a hassle with the courseload (sophomore fall we had Genetics + Orgo 2, which was the worst combo of classes in the major). If anything, getting some research under your belt earlier on could give you a higher chance of presentations/abstracts/publications later on in your undergrad career, which would be beneficial if you are really set on the "big name" med schools.
One caveat: Just be sure not to slack off on the clinical and non-clinical volunteering, as these should be the biggest chunk of your application (generally).