How to uninstall iOS 13

The easiest way to remove the public beta is to delete the beta profile, then wait for the next software update. Here's what to do:

Go to Settings > General, and tap Profiles & Device Managment.

Tap the iOS Beta Software Profile.

Tap Remove Profile, then restart your device.

Thanks

https://support.apple.com/kb/ph12521?locale=en_US

Be sure to remove the beta profile first.

You are going to lose all data you’ve added since that date.

You will have to do an iTunes restore back to iOS 12.3.1. Hopefully you already made a backup before installing iOS 13, if not you will have to start as a new iPhone.

check this

https://support.apple.com/en-us/HT203282

I have no idea what a "last update on mobile ?" means.

You can remove the profile and try Restoring your iPhone from your iCloud backup assuming you have not done an iCloud backup using iOS 13.

if you bought a new iPhone and set it up from your May backup it will have your data up to that May backup and nothing else. If you back up your iPhone now with iOS 13 on it you would not be able to set up a new iPhone with iOS 12.x on it.

How to uninstall iOS beta software - Apple Support

https://support.apple.com/en-us/HT203282

Without a computer! That was something you failed to mention.

when was the last time you backed up to iCloud?

Again, when was the last time you backed up to iCloud? If it was after you installed iOS 13 it will be of no help to you.

As it states in the link provided, "If you don't want to wait for a software update to install a non-beta version of iOS, follow the steps to restore". That said, you need to move onto the steps in the following article. Hopefully, you performed an iTunes and/or iCloud backup of your phone prior to installing the beta, as you can't install a iOS 13 beta backup to your phone, after you downgrade to iOS 12.3.1.

Remove the developer beta by restoring your device - Apple Support