My headphones are the Razer Kraken been using them for 1-2 years , I have tried using them backwards but they end up picking up a lot of background noise.
I looked around in Device Manager and did not find a way to swap the left and right outputs. Perhaps your headphone's plug is wired incorrectly. Do you have a set of earbuds you could test in your computer? Or borrow someone else's headphones to test?
Are you using a laptop or a desktop computer? If a desktop, front panel or rear panel audio connections? Which version of the Razer do you have, the usb or 3.5mm combination plug?