For shadowing, I would say you can either reach out to ANY sort of connections you may have (doctors typically don't mind some shadowing), or just make cold calls. I lined up some shadowing simply by calling around and hoping for the best. Stick with it.
Research is a little trickier, especially if you're not in school. In fact, if you don't have any research experience and you aren't in school, I think it's in your best interest to check with your alma mater for help. Beyond that, it may be difficult to find something.