Expanding battery?

There is no way for anyone to diagnose this sort of issue from an internet forum post. You need to take it in to Apple for a free hardware evaluation. Given the age of that phone, yes, it very well could be a worn out and now swelling battery, which is a potentially hazardous situation.

If it is out of warranty and the battery is just worn out, the normal battery replacement fee will apply. Batteries wear out. Lithium batteries are somewhat prone to swelling when they are old and are at the end of their useful lifespan.

Same thing happened to me with an iPhone 4. I was asked, if I always put it on a charger when not using it and I did and he said that was why it grew, lol. I don't know if that was the reason but I suspect all batteries are not created equal. You just might have a bad battery or something. It shouldn't cost that much to replace the battery.

Thanks, for that bit of info about the battery.