Battery says it's drained when it's not

A few days ago I picked up my phone and discovered it would not turn on. The battery was dead. Which was weird as I figured it had about 50% charge left. Sure enough, as soon as I plugged it in to charge it, the battery said 55%. I have since gotten low battery warnings twice, plugged my phone to charge and then gotten 55-56% full readings immediately

For example, this morning, before I plugged my phone in it said 13%, but as soon as I plugged it in I got the 56% reading. I then unplugged my phone. Unplugged, it still says 56%.

Will a full discharge fix this? I'm not even sure if I can manage a full discharge as the phone acted like the battery was fully discharged when it wasn't. Head to an Apple store for an exchange?