Does a copyright have to be filed?

No, it doesn’t have to be filed. It just has to be created. It just has to be an original work that you’ve created. And if you want to, you can put that little C in a circle, your name and the year of first publication, but that’s not essential. That might have some procedural benefits in terms of a lawsuit and the damages you can collect, but it’s not essential to there actually being a protectable copyright in your work.