There have been many posts on the MacRumors forums with users complaining of the same problem. It seems to be only affecting AT&T users as other users on T-Mobile or Verizon’s network aren’t reporting anything similar themselves. According to one of the forum goers who contacted AT&T’s tech support, the rep said that they have been receiving many calls similar in nature.
They go on to state that this is an issue with iOS 9 and iOS 9.0.1 and that iOS 9.0.2, which was recently released, should have addressed the problem. However as we can see from the various complaints, updating to iOS 9.0.2 does not seem to have helped. Perhaps it could be a location issue where only some parts of the US are affected.
So far the issue seems to come and go. Some users report that the issue has gone away for them and that they can download apps and stream music just fine, while others are still running into issues, but hopefully it will be cleared up in the next few days.