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Boot your phone in safe mode,see if anything improves:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
If you experience the same behavior in safe mode I suggest that you try to reinstall/repair the software using PC Companion:
http://www.sonymobile.com/update
In PC Companion, press start on Support Zone > Start on Update the phone/tablet software > Press the blue link that says "Repair phone/tablet".
Before repairing the software in your device you may want to backup your information first. Check out this topic for more information on how to:
http://talk.sonymobile.com/t5/FAQ/Backup-amp-Transfer/m-p/407253#U407253