Hey, this is a really good question! There definitely is an overlap between the two disciplines in the field of health law — so looking at the regulation of the health industry, representing patients/providers, and developing health policy. UCLA offers a law/public health concurrent degree and UC San Diego offers a Health Law degree.
It may be worth reaching out to these programs (or the faculty who teach there) and seeing if they can tell you more about what you could do at the intersection of these fields — or if there are other ways of connecting medicine and law.
If you are interested in seeing what other joint/concurrent degree programs are offered with medicine or law, you can take a peek at UC’s degree search tool.
Does anyone out there in the tumblr-sphere have experience with law and medicine or other advice?