Hi, is this for a Work/School account, or a Personal Microsoft account?
Try tapping on your account in the Microsoft Authenticator app, does it show just a person icon ("Personal"/Microsoft account), or does it show a person with a lanyard (Work/School account)
- Personal/Microsoft Account
- Work/School/Organization/Azure AD Account
Once you tap into that account, does it mention any of these options, or is it greyed out and won't let you tap into the account?
- Notifications Enabled
- Passwordless sign-in Enabled
- One-Time Password Code (And how many digits, 6 or 8)
- Set-Up/Disable Phone Sign-In
- Change Password
- Update Security Info
- Review Recent Activity
If it is for Work/School - your IT Administrators or HelpDesk may be able to help you reset.
Otherwise, you mentioned you can get signed into the account somewhere. You may be able to add a new Security Info method from that machine and then use that to verify later to reset your password.
If none of those options are helping, then can you double-check your current password in an Incognito Window in Edge.
Otherwise, you can try the usual methods of checking Junk/Spam folders with your recovery email / Cell service providers, but past that if you aren't receiving the Text messages or Emails, then you may need to contact your provider.