I'm confused!
While it's possible to download iTunes from the Microsoft website, which might well require you to log into your Microsoft account, iTunes itself is an Apple program, so you shouldn't need to go anywhere near to your Microsoft account to get it. (Indeed, there's no need to have a Microsoft account at all). Downloading the program directly from the Apple website should be all that you need to do:
https://www.apple.com/uk/itunes/download/
However it's worth remembering that the technical press (such as Computer Active and Web User magazines) always include iTunes in their lists of programs which should NEVER be on anyone's computer. It's horrid! MusicBee is far better:
https://www.getmusicbee.com/