Windows switched my e-mail after using xbox live app.

Please follow this suggestions as per my screenshots
Try first the start button and sign out presuming it is signed in with your sons account
Perform a full shutdown
When you then get to the sign in screen - Windows 10 always loads the last signed in user, but are other accounts not shown to the lower left of the sign in screen

If that does not then solve it please proceed to the XBox - shown on the other screenshot

Not knowing the age of your son, is his account a full user account or a child account.

If all that fails go here
https://www.google.co.uk/url?sa=t&rc...plBHyp13Kh7qCc

and verify the microsoft account email is SHOWN as yours sons
If so change it to yours

When you say there was an error message -, I presume that refers to
the account is not verified
Is that correct please

Have you signed out of the XBox Game Bar OR signed your son out
Select Settings.
Select Sign Out.
Select Sign In.
Under Use another account, select the Microsoft account that you want to sign in with.
If prompted, enter the credentials associated with that Microsoft account.

Hi, you will need to contact Microsoft Support Click Contact support
https://support.microsoft.com/en-us
Users cannot unlink accounts as it is changing another person's email address

If you are not familiar with finding the contact us
This may make it easier
https://support.microsoft.com/contactus

Could you confirm please that both your account and your sons account are independent Microsoft accounts and his is not a child account - or was and it was never changed
Also - do you have a local account for this computer - as well as a Microsoft account
If by chance you do

Open Settings > Accounts and click Your info.
After confirming that the account is set up to use a Microsoft account, click Sign in with a local account instead.
Enter the password for your Microsoft account to confirm that you're authorized to make the change, and then click Next.
On the Switch To A Local Account page, enter your new local user name and password, along with a password hint, as shown here.
Click Next to sign out from the Microsoft account and sign back in using your new local account.

It says his account isn't verified. Could that be part of the issue? I have no ability to select a local account.

Yes I know about the account not verified as we explored that before
I thought you were going to have him verify it or try to when he came home - post 3 refers

Then after that I thought you were going to contact Microsoft support on the link I gave you.

If you do not have a local account already established and you cannot sign into windows WITH your Microsoft account not an account linked to your sons - then Microsoft support is the easier way

To list it again
https://support.microsoft.com/contactus/#
and then click contact support on that page

at first you are with a virtual agent, but when you explain the situation you should end up talking to a real person, although that may be limited to certain hours, but the virtual chat should advise of the position