If you have a way to order the underworks binders, either the tri top or the ones that look like tank tops, your parents wouldn't know they're 'binders'. The tri top kind of looks like a sports bra only a bit longer, and the others look like a tank. I doubt they could tell they're compression though unless they touched them. They're in the $30 range. Another option that wouldn't be conspicuous as a binder are the back support belts. Unless your parents saw it being used as a 'bra' they wouldn't really notice it in your room and if they did well, it's back support! A Frog Bra might work also (I don't have one, I do have both types of underworks binders as well as a back support one.
Jay