Wow. I think you may need to take the phone back....I have never had a phone that the power button has done that on and especially when the phone is so new..
With this app you only have to press the app icon (i have the icon on the main homscreen) and the display shuts off. It's really simple and works great to avoid having to constantly fiddle around looking for and touching the power button .
I don't know of an app that would allow you to turn the display on from sleep and bypass using the power button.
But again, if the power button is loose after only a few weeks that's more of a hardware issue and you should return the device for a replacement.