I emailed a bunch of deans at NYU Med (I go to NYU), and one of them responded favorably, so im shadowing (actually, the dean who got me the position said not to call it shadowing, as I should not want to be in anyone's shadow. He said to call it an internship, espically since I will be doing research) there over the summer.
If your uni has a med school, try contacting some people via email, or calling them, or even just showing up and asking to speak to whomever would be in charge of shadowing.