Once a photo is posted, unless it's somehow legally protected, it's free for anyone to use. People post fake photos and "Am I pretty?" on Yahoo all the time, most of them stock (modeling) photos.
Can you give the link to something the person has posted while pretending to be you?
Are you saying that someone is pretending to be you and posting statements that YOU are a pedophile? The person is claiming to be you, making statements that he/she is then going to report to the Police as statements you have made? That would be a very easy matter to resolve- Reposting (public disclosure of private "facts”) is actionable ONLY if the "facts" are false. Yes, if this person is making up "facts," yes, there are legal steps you can take. You would only need to prove that what is being posted is false, that the person is not quoting you.
For example, if I posted I'm a felon and served time in jail (or a mental hospital) and someone picked up on that and responded to something else with those FACTS, that is not defamation. Someone would be reposting what I had admitted.
Ask an attorney. Of course, information that YOU have made public, information that YOU have disclosed, is not actionable.
What does this person have to gain by pretending to be you and confessing to being a pedophile?
Or is someone using your photo in one context or another?
I don't know what you're saying.