It seems that your disk still has the errors which prevent from mounting it read-write.
Perform the following steps:
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Boot from a Live Installer Media
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Open a Terminal and type:
sudo blkid
This will yield some output. We need to determine which device contains your root partition. It will look something like:
Look for the device with the label “ostree” and a device name like
/dev/sd…. In my case the root device is /dev/vda2 (as it’s a virtual machine). Now enter:
sudo fsck -y -c /dev/vda2
(Substitute the device name)
This will take some time as it checks the entire filesystem structure:
Now try to mount the filesystem in question to see if it has been fixed by:
sudo mount /dev/vda2 /mnt
If the command above yielded no error, chances are good that the repair was successful. In this case, reboot your machine with
reboot
If it was not successfull, run:
journalctl -k -l -n 20
This will output the last 20 lines of the kernel message buffer, which should include some indication that the device has a hardware defect. Take a photo of it and upload it here.