I haven't done this, sorry. But I don't think you need to self-flagellate by telling people you lied. The only purpose that would serve is to punish yourself, and it sounds like you feel bad enough. While I haven't lied about this sort of thing, I have lied about other things that cause me guilt. I am not proud of it, but I also try not to dwell on it since the lie itself hurt nobody. I just try to remember how bad I felt due to lying, so that I am less tempted to make the same mistake again.