Try below given steps to fix the issue of Headphones not showing up in Windows 10:- 

• First of all, try  manually enable the headphone device.
• If the headphone device is not shown in the device manager, you may need to install the driver.
• However, this method is not the best solution for the problem if your headphones are not showing up.
• This solution may only be temporary and may not work if you can't afford to buy a new one.

Also visit here:- 

https://www.articleted.com/article/453116/113616/Best-Ways-to-Fix-Headphones-Are-Not-Showing-in-Windows-10-Issues

https://educatorpages.com/site/worldzo/pages/fixes-for-headphone-not-working-in-windows-10?

https://worldzo.hpage.com/fix-headphones-not-showing-up-in-playback-devices-in-windows-10.html

http://worldzo.bravesites.com/entries/windows/headphones-not-working-in-windows-here-are-some-fixes