For a while I've had an issue where Minecraft game audio won't feed through my headphones. They work when I'm using them for any other game or application. I can even be listening to a video on my headphones at the same time as Minecraft plays on my computer speakers. The problem persists even when I use a different launcher.
If it's any help, I have found that if you change the current audio device while Minecraft (launcher) is running, it still uses the audio device that was active at the time Minecraft started. I had to exit Minecraft, including the launcher, in order for Minecraft to use the newly selected device.