I have a 6s 32GB. Since I upgraded to ios10, I can't get My Photostream to work. The pictures won't even go in to the My Photostream Folder on the phone when I snap a photo.
That is indeed strange. I don't think you are doing anything wrong. Apple website has some steps to troubleshoot which you may try here. If that doesn't work, I'd suggest chatting with Apple customer service.