Corrupt boot drive

Hi all,

So I opened my laptop today to a frozen login screen and the fans started going crazy so I did a forced shutdown. When I tried to boot up my laptop again I got the dreaded question mark folder flashing. I've tried to do all the basic 'recovery mode, disk util, verify and repair etc' but just keeps giving me errors like this:

I've got OSX loaded on a temp external drive so I'm using that at the moment. I've also installed brew and gdisk as I've seen that's helped others but I'm not 100% sure how to use it correctly.

I've got a Time Machine backup from about 6 months ago if I have to revert to it but I really want to try and recover this one as I have a lot of files I'd really love back (hours of work I don't want to do again)

Any help would be greatly appreciated

Cheers