iPhone 4s screen shaking

I've had my iPhone 4s for a little over a week. Two days ago the screen started shaking. It began as just a little up-and-down jitter right when the display lit up, then the shaking got worse and worse over several hours, until the display was showing multiple times (while still shaking and distorted) on the screen. When it got so bad I couldn't use the screen anymore, I tried to restart it and the screen just went blank white. It wouldn't turn off or restart and the screen started getting vertical black and multicolored lines, more and more of them over the course of a couple of hours, until it was almost black, but it still wouldn't shut off. I finally gave up and just let the battery die on its own. When it died completely, I plugged it in and after charging it for about 5 minutes, it booted right back up like nothing had happened. It worked normally for about 48 hours, but the screen started shaking again about 2 hours ago. I hooked it up to my laptop and restored the settings and completely re-synched all my apps, music, etc. back onto it, but it's still doing the shaking thing, which once again seems to be getting worse. So restoring it doesn't work. Is anyone else having this problem?