My account is being used by somebody else?

As stated by others try to use the 2 stage verification for added level of security.

Also as with all apps, services etc regularly change your password. I know it's a pain, as you go through life with work and utilities apps as well as all the social networks and fun apps etc but it is something that you / we all need to do. Try to use different
passwords as otherwise one site compromised could lead to others being accessed.

Staying safe online is very important. Hope its resolved soon for you

"Could this be some weird glitch? Or is somebody actually using my account?"

I doubt its a glitch, and yes, someone could be using your account if you have disclosed your account details.

As soon as you can, change the password to your account and put 2FA (2 Factor Authorization) in place, so that you are the only one able to access the account.

Use strong passwords and assign a controller passkey to ensure safety of your XBox console and your account.

Along with all the advice - also ensure you delete payment options that you may have stored on your account until you can get it reset.

you can check to see whether anyone has signed into your account by going to https://account.microsoft.com/security/ and clicking on
Sign-in activity.

Did you follow support advice and change password? I would also recommend 2 stage verification