I am having lots of different problems with my iPod touch and don't know what to do about any!

I got my iPod touch on Christmas last year, and its worked well until recentley. It has been really slow, and somehow the screen is actually coming off. To help with the slowness, I thought upgrading to the ios 6 or whatever it is would help, but it hasn't. I'm not using even more than half of my memory. The apps are all up to date, but the notifications sometimes don't show up until awhile after they happen. Should I look into getting a new iPod all together or can I trade it for a new one or something? Does it have a warranty? I use it all the time and really dont want to have to not be able to use it at all! Please help!!