Will the repentant woman be exposed after her repentance and confession of sins to some people, especially with her fear of the spread of scandal, and is this confession considered a self-exposure that causes Allah to expose her?

Openly committing a sin is forbidden, and one is obligated to conceal their own sins. However, informing about a sin for a beneficial purpose, such as seeking help for repentance, does not fall under blameworthy open disclosure. The scholars have stipulated that the blameworthy disclosure is that which occurs as a form of open defiance and mockery, not as a question or an inquiry seeking a fatwa (definition). Repentance erases what came before it, and the one who repents from a sin is like one who has no sin. A repentant person is not punished for their sin, neither in this world nor in the Hereafter.