Here's why Amelia won't tell him: there's a 50/50 chance Carter would remember them and if he doesn't it would hurt both of them. Also she does not know why he doesn't remember her so telling him everything without any solid proof can be dangerous to his health. Again if you tell someone the things they forget they will believe you but they are highly likely to remember it. She wants him to remember her as his mate not pressurise into accepting her as his mate. Hope this helps!