If I come clean, will it erode her trust?

Tell her. It's not important, so it won't devastate her trust completely or anything dramatic like that. In fact, if you handle it right, you can make it work to your advantage. Make it really clear how important it is to you that you're always honest with her, and how it bothers her that you ever said something untrue, and that you have no idea why you did it, but that you want to tell her so that she knows she can trust you always. It could be a Hollywood moment. :P