Is there a way to make your headset audio louder in one ear?

No there isn't a way to do that. It's a good idea, though. I would suggest posting this on the Xbox Requests Reddit page.

https://www.reddit.com/r/xboxinsiders/comments/1cu98ei/xbox_requests_week_of_may_17th_2024/

Hi, make sure the headsets supports game audio. There is a lot of headset like the one ear headsets that will only support party chat. if possible if you can share the headset brand names and how you are connecting them to your xbox or controller.

Third party headset makers have no choice but to wait until Microsoft releases the Headset Adaptor which suits the way in which this new audio technology is distributed to the mass populace. Microsoft are demanding everyone buys a new headset with audio
adaptor bundled i.e. headphones that are tuned to provide the highest quality audio from the Xbox One™ Audio Adapter. The Titanfall Ear Force Atlas Official Gaming Headset, Ear Force XO7 and Ear Force XO4 have been pushed back to March 7, 2014 at Amazon. There
is NO way we are getting Dolby Digital 5.1 over optical in the near future as it has and always been I suspect that Microsoft would have it any other way.

Update: Gaming audio will come via the Headset Audio Adaptor source
www.turtlebeach.com/.../494 making Dolby Digital optical headsets redundant. If you want game/chat audio mix for the Xbox One you have to buy a headset bundled with a audio adaptor or wait until the adaptor is released by Microsoft.

Hopefully they expand general bluetooth accessory and audio support with next gen - BUT, as a person with massively pierced ears and glasses, I'm pretty sure you should be able to find some regular headsets that work for you comfortably. I use the wireless
Plantronics Rig 800s, and they are super comfortable, have great audio quality for both chat and game audio (including the fact they come with a Dolby Atmos headphones license). The problem with single ear headsets is they generally only provide chat audio,
and cut off the directionality of your hearing by blocking off one ear to game audio. I would just try some more headsets to find one that's comfortable for you.