I typically find writing things easier than saying them, especially in terms of a first disclosure, but your mileage may vary! I've often asked for things back or to shred them because I don't want physical records of some of these things and my treatment professionals have been very understanding of that. But I know for some people writing it down is scarier. I don't think you need to share any explicit details, but I do think that disclosing could help start the process of healing.
As Auror mentioned, I would actually recommend asking your psychologist what their reporting requirements are - I just moved and found out the state I moved to recently eliminated the statute of limitations for child sexual abuse, which means that my therapist would have been legally mandated to report what happened had it not been reported before, whether or not I wanted her to. Because this is becoming more common as legal systems recognize that many children are unable to report and shouldn't have to bear that burden, I think it's a good idea to check in with any professionals about the mandatory reporting requirements where you live, just so you don't unexpectedly end up in a situation you may not want or may not be ready for.