I replace my iPhone battery with a cheap one off eBay every year or two when something else breaks. Battery life is pretty good, but the screen pops up now making the phone 0.5mm thicker. It's doing OK for a 5 year old phone, but my friends can't believe I paid $800 for an iPhone 5.
If the screen is popping up, that condition might be trigerred by a swollen battery.
My iPhone 5 also did that, after a while, it worsened so much that the screen colors became affected. I took it to an apple store, paid the fee and had them replace the battery.
IMHO a swollen battery is a huge risk, and apple should have replaced my phone without charge.
Anyways, be careful and if the battery is swollen, it's time for yet another battery change :)