FaceID has locked me out of my iPhone

See if any of the things in this article help: If you don't see a 'disabled' message but do have general issues with Face ID not working properly, explore the list of things to try in this document: If Face ID isn't working on your iPhone or iPad Pro - Apple Support

Unfortunately if you have a forgotten/unknown device passcode, or have a disabled device (device unavailable or lockout screen), you have no option but to erase the device. However, you can eventually restore the data and settings from a backup you made before the device was disabled. If you end up having to use a computer and you do not have one, borrow one from a friend, or go to an Apple Retail Store or Apple Authorized Service Provider. You can also use a PC with iTunes. You will likely also need your Apple ID and password. All Apple mobile devices follow the same general procedure but the link below and other links off it provide system and model specific instructions:

If you see an iPhone or iPad unavailable message or Security Lockout screen - Apple Support

Face ID recognition can fail for multiple reasons and that is why it also requires you to set up and remember a passcode to unlock the device. Per About Face ID advanced technology - Apple Support

To use Face ID, you must set up a passcode on your device. You must enter your passcode for additional security validation when:

• The device has just been turned on or restarted.
• The device hasn’t been unlocked for more than 48 hours.
• The passcode hasn’t been used to unlock the device in the last six and a half days and Face ID hasn't unlocked the device in the last 4 hours.
• The device has received a remote lock command.
• After five unsuccessful attempts to match a face.

If your iPhone is disabled because of too many passcode attempts, or you forgot the passcode you set up your only option is to use a computer to restore the iPhone following If you forgot your iPhone passcode - Apple Support

If after restoring following the above steps your Face ID still doesn't work and it's a hardware issue that needs repaired, please see #9 at If Face ID isn't working on your iPhone or iPad Pro - Apple Support

Face ID did not lock you out of your phone. You did that yourself by entering the passcode incorrectly too many times when prompted.

Why in the world have you gone 2 months without backing up your phone?

If it’s already in security lockout, your only option is to erase and restore the phone. Any data that was not backed up or synced to the cloud is gone.