Sensitivity on screen of iPhone 6 plus?

My screen seems to not respond well at certain times. A lot of times it won't enter the space that I press during typing and it won't respond to something pushed in an interactive webpage for instance. I am on iOS 8.3 I do have a tempered glass screen protector and I have the bodyguardz one. Could that affect it? Also at random times it will just shut out of a game or a webpage and go back to main screen but if I end everything and go back in it will work again..