How should I deepen my knowledge of medical issues?

I'd recommend setting aside a free period a week to think about medical issues. This could look like reading a book about a medical issue or reading through the Health section on the BBC. As you read the website, if you find an articles which particularly interest you, look into it more! For example, you could look at the journal article the news is reporting on or find another news article on it which could have an alternative perspective on the issue.
If you want, I can provide a reading list which could get you started in terms of books to read.