I Was told by an iTunes Sr. Advisor that "Apple really dropped the ball on this one" after 5-6 hours on the phone. They told me not to bother going to an Apple Store because this isn't hardware related, that it's an issue with iOS 9.1, although neither of the two 9.2 betas fix this in any way at all. Two different iPhones both with the same problem as soon as 9.1 was installed. I had my iPhone connected to my MacBook Pro and was sharing my iPhone's screen through QuickTime and the Apple tech was connected through Screen Sharing. We set my iph 6S up as new, created a new iTunes account and everything worked fine when I tried downloading some other free apps. We again set it up as a new phone and then I signed in with my regular/normal iTunes account and it wasn't working; same issues as everyone else.
I've also noticed that any photos I've added in the photo app on my MacBook Pro show that they've been uploaded, but when I go to iCloud.com/#photos, nothing I've added are there. Music I've added to my iTunes library looks like it's been matched, but I can't tell if it has. Nothing plays on my 2nd device, my Apple TV isn't showing any updated music, and my iPhone doesn't show any music at all. iTunes shows that I can listen to music through the cloud, though, like how it does for my bookmarks and stuff under the info section.
One of the techs I spoke to told me to just create a new Apple ID. Knowing the answers ahead of time, I asked her if ALL 1187 of my Apps would be available on that account for me to download. She said no. I asked if my iTunes Match library would be available under that account, and she said no. I asked her if all of the movies and TV shows I've purchased would be available, and she literally told me, "Yeah, I get it.." and I said "Apparently you don't!"
So yeah. I was told not even to go to the Apple Store because they have no solution.