To buy diapers as a teen without your mom or parents noticing you can do so by going to a store such as Walmart, Dollar General etc and put the diapers in a backpack and that way you could bring them inside your house without being noticed.
Or order online and if you order diapers from a medical supply place they will ship the diapers discretely.
Say it's a present from someone or just say you ordered something for your computer, room etc.
Then hide the diapers such as in your closest, behind some clothes or in a tote that nobody looks in.
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.