Why does only one of my headphones work

assuming you have tried multiple headphones, and the headset jack you replaced it with are fully functional, Than the issue will lay in the processing of the headset jack itself. at that point, there are unfortunately only two more possibilities,

1) Software:

a) Setting problem. If you set your sound settings to Mono, or if you have accessability options set to turn one speaker off, you will need to change those

b) External software corruption. this is fixed by a factory reset.

c) Core software failure. This will need to reload stock OS from Odin in download mode.

2) Motherboard:

a) check for damage physical damage under microscope. (10X suggested)

b) Replace Board