macos – Problems logging into Mac after reinstalling older OS

I’m having problems with my late 2013 27 inch Mac and need some help.

Last night I tried to install a newer OS (Mojave) and it told me there was a disk management error (69854). I was previously on OS High Sierra.

I followed all the troubleshooting guides etc. and eventually had to
resinstall the OS in recovery mode. It took me all the way back to OS X Mavericks I think.

Unfortunately I don’t have a time machine backup. OS X is installed but it won’t let me go past the login page. When I try to enter my password the screen refreshes and nothing happens.

I’m inexperienced with this sort of stuff so any easy to follow help would be appreciated.

In terms of logging back in, I’ve repaired the “disc permissions” in disk utility but it’s done nothing.