I don't work for Adobe, but what MAY work is...
Sign OUT of your existing paid account
Redeem the code your school gives you so you have a new account using your school email
Sign IN to your new account
The sign out/in process is what I have seen described when more than one person uses the same computer, so "A" and "B" each has his/her account active
Log out of your Cloud account... Restart your computer... Log in to your paid Cloud account
So, my current account uses my school email because I got the education pricing. Any other ideas?