I had the same problem. Mbp still under warranty till 2018. Found out my battery is slightly bloated, went down to apple shop for them to diagnose.
During the check up, they also noticed something wrong with my LCD panel, supposedly something to do with the coating on the panel.
In the end I got to change my battery and a new LCD panel foc.
battery swollen is a different problem, I believe it is considered as product defect which is covered by AppleCare for sure. I had this experience too, my late 2013 rMBP battery was swelling last year, hard to press/click the touchpad, I sent it to a.lab, and they replaced battery, touchpad and keyboard for free.
"service battery" could be a product defect too, or just a normal operation loss, will see what they will say...
