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Contact Tableau Support--I'm not sure if you can do this or not, but I don't think there is a way to do it through the website without Tableau's help. I could be wrong, but I couldn't find a way.
I figured it out! I created a new Tableau Public account with my updated email address here: https://public.tableausoftware.com/auth/signup.
Then, in my existing workbook, I went to 'save as' and when the dialogue box popped up to log in, I simply logged in with my new email address account (instead of the one I created the workbook under) and was able to save all my work to the new account. Hope this helps if anyone else is having similar problems.