iPhone 6 Battery Expanding I have an iPhone 6, without Apple Care.

A few months ago I noticed it got unbelievably, incredibly hot during use, both on and off the charger. It would also use the battery quite fast, up to 2% a minute sometimes, and would often be completely depleted by midday from a full charge, after it being in my pocket at school with time and social media checks being the only use. It also was in mint condition, having lived in a Lifeproof case for its entire life. 

However, I noticed the case started to bulge just underneath the left volume button on the side, pushing outwards slightly. Could this be a battery problem? Apple Support told me my battery health was fine (90%), so I should go to an Apple Store to get it looked at. As the closest store is 4 hours away, could anyone tell me if this is battery related or not?
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!