The reason your screen looks as if it is coming unglued is because you maybe dropped your iphone on an edge and it became dented. When the iphone casing is dented it may make the screen pull away from the plastic outer shell. That could also be the reason why you have white spots on your phone screen. Your screen may be pulling away from the digitizer behind it. To fix this you'll most likely have to repair your phone screen.
The most likely problem that you are having is that the phillips head screw driver you are using is stripped or the screw is stripped and that is making it difficult to turn the screw. I had that problem and thought that it was just me. I bought a new repair kit and my new tools fit perfectly to the screws without any problems