I really should have raised this sooner, but I kept forgetting. Ever since I installed iOS9 on my iPhone 6, it has been stuck in silent/vibrate mode. Previously, in iOS 8, the side switch would toggle the silent mode on and off. Ever since the first drop of iOS9 though, that switch inexplicably changed operation to control orientation lock (which frankly is useless to me and it used to be just a button away on the control center screen) and now I can find no way anywhere to take my phone off silent. It was in silent mode when I installed iOS 9. I've looked in the control center for a new button to toggle silent/vibrate, i've scoured the many settings looking for a setting to change it or a setting to change the operation of the switch but couldn't find anything (though the settings can be overwhelming and I might have missed it).
Then you seem to be in the same boat as this guy: https://forums.developer.apple.com/message/38472
Your best bet would be to go to Settings > General > Reset > Reset All Settings. Obviously you'll have to redo your iPhone's system settings afterwards so I don't know if you feel it's a good trade-off (there's no guarantee it will work)