Get another email address from somewhere like AOL or Yahoo and use the steps in the article below to change the old Apple ID email address to the new email address. That will free up your private email address so you can use it to replace your work email address.
Apple hasn’t published any guidance for using an address again. Normally, if your e-mail address was associated with an ID in any way, then it can't be reused as an Apple ID email address for approximately one year. I have also seen posts that stated Apple told them there was a 30 day waiting period before the address could be used again. You can try waiting 30 days to see if that works.
Note the restrictions in the article.
Apple ID Name Change. *
Make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.
What to do after you change your Apple ID or password - Apple Support * I suggest doing this before you change your Apple ID or password.