According to wikipedia that there are not many courses or career paths specifically on medical journalism, but it is hard to imagine that this field is not going to expand in future.
Recently the McMaster Daily News reported on a YouTube channel called ViolinMD created by Dr. Siobhan Deshauer. She was a fifth year medical resident (recently finished residency successfully) but has been vlogging about her experience quite frequently since she started residency. She was a graduate of the Michael G. DeGroote school of medicine, which is why you can get a BA in music (violin) and still get into a medical school like McMaster. In one of the episodes she mentions "medical journalism" as she did a stint doing such for ABC news as a consultant on their medical news team. I can't recall that specific episode - because I have watched so many of them - but we can imagine that one of the reasons she got that consultancy work was because of her creative media skills vlogging her real lived experience on the front lines.
In Canada one of the most famous medical journalists might be Andre Picard, health columnist for the Globe and Mail. His recent book "Neglected No More:The Urgent Need to Improve the Lives of Canada's Elders in the Wake of a Pandemic", shed a lot of light on the state of long term care in the Canadian system.
There is a health column in the New York times called "Diagnosis" written by Lisa Sanders MD, who used write scripts for the TV Series House. I watched the TV documentary version of it about solving rare medical mysteries, like it is detective work. Of course there are the likes of Sanjay Gupta, Chief Medical Correspondent for CNN, etc.
There are also investigative journalism books that really delve into medical issues. Michael Pollan wrote "How to Change Your Mind: What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence" which is a master study of psychedelics research. The book by author James Nestor called "Breath: The New Science of a Lost Art" is a pioneering investigation into the new research and evidence on human breathing and the effect on our overall health. It is fascinating to see how these science minded though "non-health practitioners" explore these fields so relevant to medical well being. There are many more books by journalists that explore medical and health issues.
An area tangential to all this are the scientists who study the reporting of health information in various media looking for evidence of factual inaccuracy, let alone stories that create false hope or deceive the public. Timothy Caulfield is famous for debunking the myths and misconceptions, and the McMaster Health Forum has an evidence based health research group focusing on policy decision making for various health topics of concern.