Mailing a copy to yourself is not the same as copyright registration and is not a form of copyright registration, nor is it a reliable form of evidence of copyright ownership because there are several ways with which registered mail can be tampered with (for example, mailing yourself an unsealed envelope and entering contents at a later date).
There is no harm in mailing yourself your own work, but it will likely not be given serious consideration in the event of a legal dispute.
One thing you can do to help support a claim of copyright is saving the different versions of your work on your computer, beginning with the earliest, and maintain back up files. Of course, if the other individual has computer files with original content predating yours, you will not win a lawsuit unless you have compelling evidence of copyright infringement.
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