Does one incur sin by saying, "I did such and such" (a sin, a transgression, a crime)?

Openly committing a sin is an iniquity that necessitates repentance, for the entire Ummah is forgiven except for those who publicize their sins. It is not permissible for a person to publicize their sin unless there is an overriding benefit. So, if your disclosure of your sin is without benefit, it is a sin; but if it is for a benefit, then there is no blame in it.