Welcome.
Being only a year older than yourself, I've faced similar issues. If you really do want the diapers and want to keep them private, you'll have to find a really good hiding place. You know your house better than anyone else. If your closet isn't private enough, perhaps somewhere else is. Personally, my closet works great. However, if I feel that it may not be good enough at some point in time (usually when friends are coming over), I use the garage. There's sort of a loft in there and I'm the only one that can get to it (neither of my parents can get up the ladder).
If something like that won't work, how about under your matress? Take all of the diapers out of the pack and stash them under your matress (stacking them only one or two high). You could also invest in a lockable trunk and put them in there.
Good luck.