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Do you have any 3rd party screen protector on the phone? In that case try to remove it to see if your touch works better.
Try to start the phone in safe mode to see if the problem may be related to any 3rd party app installed in your phone:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
You can also test the touch function using the Xperia diagnostic app:
https://play.google.com/store/apps/details?id=com.sonymobile.androidapp.functiontester