Please clear the EA App's cache again:
https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/
Then restart your computer, and create a new folder into which you'll install Sims Medieval. The folder should be on the root level of the drive, e.g. C:\Games is fine, but not C:\Program Files\Games.
If you use a third-party antivirus, disable it before trying to install the game. As long as you don't do anything else at the same time, your computer should be safe.
If this doesn't help, let me know whether the drive you're using is internal or external, and if external, what format it has. You can see this in Disk Management; hit Windows key-X to see the option to open it.