I suspect my Late 2013 MacBook Pro battery is swollen because it doesn't sit flat on flat surface, trackpad isn't working properly and unable to close my screen

Can anyone recommend me place to fix my MacBook Pro with reasonable price and trustable service?
And also does anyone has any idea how much would it cost to repair and facing the same problem?

Do you guys think I could get free repair from Apple even the warranty is expired? Battery cycle count is 124 only...