I can say for sure your issue, but I have seen very similar before, and what has likely happened is that your personal email was added as an alternate email in

I can say for sure your issue, but I have seen very similar before, and what has likely happened is that your personal email was added as an alternate email in their tenant, sometimes this is for account recovery or MFA. If you have your daughter login to her school account, and remove your email from her account. Your account will revert to a normal microsoft account. You will however have very limited access to azure with a personal account, and doing things like registering an app is going to be unlikely unless you have your own tenant, or added to some other tenant.