Chosen Solution
Why is my screen bulging on the left side of the case?
Yes it more than likely is a swollen battery. If you have a replacement battery, open the device with the proper tools and after you unhook the battery and LCD, check the battery for its size and shape. If the phone is laying flat on a desk, get down to phone level and look at it and see if you notice it protruding higher on that side than the other. If it is the battery and you replace it, the LCD will sit properly in the phone again and will look normal. Hope this helps :)
Most likely is a bad swollen battery. Here’s how to replace it: iPhone 6 Battery Replacement