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Every time I touch my iPhone 5s display it turns a white tint and when I push it becomes very whitish, is the battery swelling and pushing on the LCD? The screen is sort of pushing out. Do I just get a new battery or a new screen? Any ideas?

The screen pushing out is an indicator of a swelling battery. Turn off the phone, get the battery out of the phone(follow safety precautions), and replace the battery(you can get a new battery here).