Iphone 5c keyboard lag and screen problems

i have a 16 gb white 5c Iphone, newly bought,about a month ago and i am having issues with my keyboard and screen.There is a lag for about 10-15 sec for whatever letter i type on the keyboard and if i try to press home screen or anything else it stucks completely and the screen goes off and on repeatedly and when it goes on it shows the same image it was showing before it went off (just the screen not the device) until after 5-10 minutes the device restarts.I tried resetting the settings,restoring the device,but no results.I even went to an Apple store and they didn't know what to do,just told me it was probably a software problem and as so they couldn't exchange my iphone for another one.They ran some tests but still nothing and then did a "complete in-depth restore" and told me that if the problem occurred again i should go back to them.The problem still persists and i am going to see them in 2 or 3 weeks because i am busy right now.Any of you have any ideas what might be going on and have any suggestions?

Thank you in advance