I have a law degree and am now applying to med school. I would absolutely not pursue a JD unless you're really want to be a lawyer. The job market for lawyers is atrocious, and while having both degrees would give you a leg up in health law and med mal, you have much better odds of finding a job with decent pay in medicine than in law right now (and for the foreseeable future). Do a google search for "legal job market" to see what I'm talking about. Salaries have tanked, and most new grads are taking jobs that would have been laughable 10 years ago. Taking out an extra $100-200 thousand just for the possibility of finding a job that would use both doesn't make much sense to me. Also, keep in mind that law students take only 1 or 2 (or 3 at the very most) classes that pertain to healthcare in any way. Are you sure you want to take Torts, Constitutional Law, Property Law, Corporate Law, Criminal Law, etc?
JD/MD programs do exist, but since your school doesn't have one in place, and since you haven't applied to your university's law school (or taken the LSAT, I'm assuming), that's probably not an option for you.
If you're interested in law and want to somehow incorporate it into your education, you could do joint research over the summer or even audit a health law class at your local law school if you can fit it into your schedule. You could also look into doing a 1 year certificate program in health law, though I'm not sure that those programs have much worth (aside from pursuing an interest).
Sorry to be a Negative Nancy. I just would hate to see someone pour money into a degree that currently has so little value if they aren't absolutely passionate about the field.