Submerged iphone 5 in water, screen problems

WHAT HAPPENED:
Wore a new pair of jeans today with tight back pockets, phone slipped out, dropped into the toilet (before I went!) and got completely submerged.

WHAT I DID:
I panicked, grabbed it out and wrapped it in my flannel shirt. After removing the case I dried it off as best I could. Later, after it was well dried, I removed the screen protector so that nothing was stuck under there. YES, I turned it on (I didn't know you were supposed to keep it off) and it worked, but…

PROBLEM:
… The right half of the screen wasn't working. I couldn't even unlock it at first. Now I CAN unlock the phone, but I still can't open some aps on the right side of the screen, it is unresponsive.

But the scary part is the brightness. It is dim everywhere except the top quarter. I can also see these sort of streaks along the length of the screen on a white background.

SOLUTION?
What do I do! Is there a way I can clean the screen? I'm willing to take it apart if I can find a good instructional video. I have a feeling the rice won't help, as I think there's somehow moisture inside the screen. I'm also scared that if I turn off the phone, it won't turn on.
And I know I will eventually have to go to an Apple store if nothing else works, so please don't remind me. What else can I try?

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