iPhone 6 Battery Expanding
If by Could this be a battery problem? you want to know whether it's where the battery is located inside the phone, then the answer is yes. 

In an iPhone 6 the battery is located at left-centre of the device (i.e. if you're facing it with the home button at the bottom). I should mention that the top of the battery is roughly in line with the bottom of the mute switch, so it is quite possible that the battery could be the problem. However, it's impossible for us to say since we can't physically inspect it. 

You really need to get it checked out, but make sure you make a full backup first!