My iPhone 6 shakes when scrolling and presses random apps and notifications sometimes?

When I first got my iPhone 6 it worked fine but then about a day after I received it I noticed sometimes when I'm scrolling and just leave my finger on the screen it shakes and it will move up and down and sometimes open up random apps or messages, or press letters on the other side of the keyboard when I did not click it... I feel like it's just a software issue but no one else I've talked to is having the same problem so I don't know if I should go to Sprint (my carrier) or an Apple Store and see if it's a problem with the phone itself. Could anyone tell me what's going on with my phone?