jules said:
Unfortunately, registering copyright is not free, and as pointed out above can be seen as amateur.
I'd suggest showing the work to somebody independent (i.e. not a close friend or relative) who would be willing to come to court and state that they'd seen it on a particular date as the best way of dealing with this.
No, it isn't free, but it is the way the law works. And I never say to register your own work unless you're planning to self-publish, at which point it's a must do.
Showing your work to someone doesn't help, either. Unless the work is registered you cannot collect damages in court. That's just how it is.
But there's no need to worry about it simply because no one is going to steal your work. It's only after you have something published, at which point any legitimate publisher will already have registered the work, that you have to worry about plagiarism and piracy. Unpublished work is worth somewhat less than the paper it's written on. Even a Stephen King manuscript is just another manuscript once his name is removed.
Hollywood, now, there's a place you need to register and protect everything you write, though this is often as much or more for the protection of the people you're sending the work to as it is for your own protection.
Books and short stories are different. No one is going to steal them, there's nothing they could do with them if they did steal them, and face it, any agent or publisher has thousands and thousands and thousands of manuscripts pouring in on a constant basis. Stealing doesn't even cross their minds. Bonfires do, but stealing doesn't.
Just submit the work. There's zero need to worry about poor man's copyright, or about registering the work before it's published.