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Try it in Safe Mode and report back.
Next try to clear its cache:
- Go to Settings -> Apps -> All -> Camera -> Clear data and restart your phone.
I hope it does work, but if it doesn't then repair the phone with PCC, if PCC doesn't work then contact your local Xperia Care
http://support.sonymobile.com/global-en/contactUs/
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355