If you never downloaded El Capitan using your Apple ID, you won't be able to download it in the Recovery Partition.
I suggest you reboot normally, log into the App Store, and download El Capitan using the link below. Then make a bootable USB drive, which you can do using these 2 programs or Apple's instructions. Once you have that, boot off the USB drive and accomplish the steps in the 3rd link. Then reinstall the OS.
You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra or find an older computer where you can download it using your Apple ID.
Bootable USB Flash Drive – Diskmaker X Disk Creator oruse Apple’s method Create a bootable installer for OS
Selling old Mac (4)