Hi there and welcome
If you connect the headphones to the phone and then check, does it then show ringer?
ok, looks like you may have damaged the speaker, but we will do a reset of the phone to be sure its not the firmware.
This will remove any data from the phone and return it to new, but this you cannot avoid.
To do the reset.
Then setup the phone again and let me know if it now allows you to choose ringer please.
It depends on what has been backed up to this, if your data is backed up to it then yes.
I believe you need to run the app to do that first