I'm not exactly sure how the design is for being able to work on the screen. It looks like you may need a new screen.
You can purchase a new Storm 2 screen on Amazon here... Amazon.com: Blackberry 9550 002/111 Storm 2 LCD Screen + touch digitizer + Repair tools: Explore similar items
And watch the video below for how to replace the Storm 2 screen:
[Mobile? Click Here for Video]