BLUE SCREEN OF DEATH - but worse

Hi guys, I have an iPhone 5s that keeps showing the famous blue screen and rebooting, but unlike some this doesn't happen over a certain app, but ALL THE TIME. This has been going on since the minute I first turned it on, brand new, and it will only go a minute or so without rebooting. But with the blue screen comes also some white horizontal lines, and sometimes the apple logo, but messed up (I've seen it go red too, it's a very creative bug).

Also there seems to be some problem with the touch screen, that is not working in a stripe of the superior part. Aaand sometimes the touch is extremely sensitive too.

So I'm trying some troubleshooting before going to an Apple Store and trying to get a new one, specially because I'm in another country right now.

I have already tried to update it, but it somehow goes into recovery mod

e at the end (and wont come out). Also tried recovering it but it doesn't goes all the way without rebooting.

I'm really counting on some help here, since I've always been faithful to apple (even when my last iPhone was stolen). Anything helps!