How can I show that my self-published work is in the public domain? Simply by stating something like "Released into the public domain"? Or using the public domain symbol 🅮?
Laws are complicated. Consider releasing your work under CC0, which was developed by professionals to make it as easy as possible to get you work released "completely as possible in the public domain":
[W]hile no tool, not even CC0, can guarantee a complete relinquishment of all copyright and database rights in every jurisdiction, we believe it provides the best and most complete alternative for contributing a work to the public domain given the many complex and diverse copyright and database systems around the world.
(See the full description for a better explanation.)
I've seen this license used on Stack Exchange, announced in user profiles. It's important to understand a little more about why this works here: SE content is automatically licensed as CC BY-SA, but it's a non-exclusive license, so the author can dual license it. (There's no reason for your audience to not take advantage of the most permissive license when there's more than one.) Check the terms of where you're publishing to ensure that this type of licensing is possible for you. It should be possible if you're self publishing.
As for how to show this, the CC Wiki has a tool to generate HTML to announce your license. Or you can just have "Copyright and related rights waived via CC0" displayed in the description for your work.
As the author of an original piece, you can declare it is in the public domain in lieu of declaring your ownership of copyright. The phrase you used is fine. An article at stanford.edu recommends the phrase "Dedicated to the Public Domain" (search the link for the word 'Dedication' to see for yourself)
Once it is in the public domain, anyone can do anything with the text, including producing a derivative work and claiming it as their own, or selling it.
If you want others to use your work without restrictions and don't care about making $$ then you could publish it under Creative Commons License. This makes it free for anyone to use and replicate, but restricts them from selling or claiming authorship. They can extend the work, creating a kind of co-authorship situation, but the derivative works are also bound by the Creative Commons License.