Obviously conserving your data is most important. You need at least Time Machine backup and if possible an external bootable clone as well. Carbon Copy Cloner is one well known app for this.
If you also copy the High Sierra (HS) installer on to the clone disk, it can be used to erase, repair, reformat, reinstall and migrate back, your system.
Booting from outside your system and running Disk Utility (DU) "First Aid" from there, may solve the disk error problem, where using the Recovery Partition is limited. By the way, in the DU View menu, select "Show all Devices", and run the first Aid on each volume shown. The main disk often passes ok with errors needing to be fixed on the OS volume itself.
If you have not used APFS and your HDD's are still with HFS+, erasing and reformatting may not be required and the disk may repair ok.
If you cannot now access your computer, maybe a friend's clone could be used for the repairs and running the installer again. Unless you actually erase the disk, your user account should still be be there.