iPhone 6 cellular depleted because of System Services (iTunes Accounts)

I recently restored my iPhone 6 iOS software after my battery life was absolutely appalling and iPhone getting too hot. I restored the iPhone to iOS 8.4.1 and this sorted out the heating problem and battery life, but since then my cell phone data package from my service provider was completely depleted in two days. The System Services (more specifically iTunes Account) utilised 5GB of data in two days. This is a crazy amount of data and it was using this data even when my phone was not being utilised and just sitting on my desk. I usually don't even finish 5GB of data in a month, let alone 2 days, as I do all my downloading and updates from WIFI at home.

I have since then restored my iPhone 6 iOS software again, and completely turned off the cellular data to limit cell data utilisation by the iPhone. I also have signed up for the Apple Music service and think that this may be causing my high data usage, although I make all the music I want 'Available Offline' so I don't use data while listening to it at work. Has anyone else had this problem or been able to find a solution to it? I cannot afford a phone that is so reckless with data usage.

Since the iOS restores, I've also been having numerous problems with Apple Music and items not downloading and loosing my entire music catalog and downloads. Very irritating.

I shudder to think how much this is going to cost me, and how hard this will hit my pocket, as data packages are excessively expensive in South Africa.