media creation tool just lets you make a Win 10 installer on USB or DVD, I get it mainly to help booting, run repair tools and maybe to reinstall win 10 if we have no other choice. If we run installation process it will likely want to wipe C drive but if storage is on another hard drive, it won't touch it. You could use the linux CD to copy things off C onto storage if its another hdd, that way you don't lose anything valuable.
If you make the installer, in its repair menu it includes Command Prompt (CMD), you can try to run sfc /scannow, it doesn't always work from in CMD from the installer, but its worth a try.
change boot order so USB is first, hdd second
boot from installer
on screen after languages, choose repair this pc, not install.
choose troubleshoot
choose advanced
choose command prompt
type sfc /scannow and press enter
type exit once complete and restart PC and see if it helped.