I would like to continue to update my game, do I need to wait until the game jam results are done to update the game files on my itch.io page?

Yes, I think we have to wait 2 weeks before changing anything

What you could maybe do if you want to show your progress is create a different itch.io project and upload the updated version there. It won't count for the jam but at least you can show off your updates and once the voting is over you can update your main page :D

Yeah, as mentioned above, no updates until the voting period is over.  Like FaFeDev said, if you want you could create a new page and upload new builds there if you want!

Thank you :)