I'm not saying it's not a big deal - it's obviously a very big deal to you!
However, I'm not sure there's anything you can do about what was, clearly, something of an innocent mistake. She wasn't falsely arrested in the legal sense of the term; the detective was only doing his job and the physician made a mistake. The result was unfortunate, but actionable? I'm doubtful.
By all means though, have a chat with a local attorney - you might want to start with Personal Injury attorneys.
I'm also very sorry for your loss.

