Prohibition Sign and Can't Reinstall OS X
Wow. After a frustrating 6 hours, I managed to fix it 10 minutes after posting this.

Although I have no idea what I really did, I'll post my "solution" for anyone with the same problem who happens to come across this because the amount of frustration I felt at people who described my exact problem but never gave an update is unreal.

Anyways, all I did was kept restarting my computer, booting into internet recovery mode and just continuously repairing the disk over and over, ignoring the "this disk can't be repaired" and other messages. I only ran the "fsck -fy" command once in total. It looks like the key is just continuously repairing the disk until it starts to function again.

I knew it was working when it returned a success message and the disk showed up in the OS X reinstall menu, but I didn't even need to reinstall; I rebooted and everything is working fine.