My issue is now resolved, fsck didn't work because I was doing it on the wrong partition (yeah I know sorry for being dumb). It finally worked after doing
fsck /etc/sdm-2
(I thought it was sda...)
I didn't run a memtest because I didn't manage to find the option to do it despite the tutorials on the web.
Thanks again a lot everybody for the help!
EDIT: How do I put [SOLVED] in the title please?