Bag of rice is a great idea but it need more than that. Phone should be opened and dried. I would just use hairdryer lightly. Disconnect the battery then leave it in an open air for 3-4 hours
Have you pushed the screen a little too hard and too much ? Anyways email support and attach photos and you should get a replacement. There is not much else you can do
Have you tried restarting the phone by holding sleep/wake button and home button until you see apple logo. If it doesn't help try itunes restore. If all these won't work then it is a problem with connector on logic board
