If your computer doesn't have Bluetooth and your wired headphones are damaged, you can connect your Bluetooth headphones to your non-Bluetooth computer using the method I'm about to explain.
First, download the Audio Relay program from
this site. Then, download Audio Relay from here on your phone , or from the original Google Play store if you don't trust the original site. After installing it on both your phone and computer, connect your phone to the computer case with a cable. You can also connect wirelessly, but you'll experience significant audio stuttering that way. Then, on your phone: Go to Settings > Connections > Mobile Hotspot & Internet Sharing and activate the "USB connection" option, meaning activate the tethernet connection. Next, open Audio Relay on both your phone and computer. On your phone, go to "Servers" and connect to the server ending in 118 or the one below. After connecting, in the Audio Relay settings on your phone, set the audio quality to uncompressed. Set the audio output to AudioTrack. Set the cache size to custom and set it to 10. On your computer, go to "Settings" and ensure all advanced settings are enabled. To prevent the tethernet connection from being used, on your phone (in the bottom right corner) and on your computer (in the bottom right corner), click "Open Network and Internet settings". Go to "Show adapter options" and access your phone's internet. From there, click on "Properties" > "IPv4", then "Properties" > "Advanced", uncheck "Automatic measurement" and set "Interface measurement" to 5000. This will stop your phone from using your internet connection.
If you'd like to watch it as a video: