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Do you get a black screen when opening back camera? Do you have any protective case on the phone? Try to remove it in that case.
Otherwise it sounds like you should have this examined by a service center. Since you got your phone last week I suggest that you contact your local Xperia support team to see which options you have:
Reinstall the latest update with SUS or PCC, if that doesn't work then take it back to the store or to a Sony repair center
Bridge (for Mac)
Alternatives on How to backup Xperias