If you are healthy, why are you unable to leave your home? Do you mean literally never able to leave for even an hour? Why would that be, is someone preventing you from leaving?
I don't think there is any way to just order birth-control pills online, though you can probably get condoms online.
You could get an IUD. That would only be a couple of visits to the ob-gyn and then you're done. You have to have your checkups anyway. You can't be sexually active without having a doctor.