To order diapers as a teen without your parents noticing you could tell your parents that you're ordering something and are expecting a package such as a toy, game etc that comes in a larger box.
When you order diapers online through medical places they will ship in discrete boxes without any mention of diapers.
Or if you order a sample of bambinodiapers they will come in an envelope that you cannot see through and it could be passed off as ordering shirts.
When I first ordered a sample of bambinodiapers I was living with my parents and it came in a plastic sleeve envelope and was very discrete.
I just told my parents I ordered a few shirts and they believed it.
As for boxes I also ordered a box of diapers through medical websites and they always came in a plain brown box and had no mention of diapers.
I just passed it off as being some games, computer parts etc.
Or I would sometimes say it was a gift from someone or I bought a gift for someone and then they never said anything else.
Another option is to go to Dollar General and get some size 7 Gentle Steps diapers which are good diapers.
As a teen you should be able to fit in them somewhat and depending on your age you may actually fit into them if you're skinning enough.
You could place the diapers in a backpack and then bring them into your house that way.