If you can enter the General Test Menu, you can check if your screen is registering exactly where you are touching.
Pull up the phones dial pad and dial *#0*#
To get to the test menu.
Select Touch
Should see a screen with small boxes around the edge of screen and a X of boxes in the center.
Touch any of the boxes and they will turn green and a black dot will show actual contact point.
Try different boxes around the screen to see how it registers.
You can drag your finger through the boxes
When all the boxes are green, it will return to the test menu.
Tap the return/ back button twice to exit test menu