IP Widget Mail Plugin

This is no standalone app. You need to install IP Widget (https://play.google.com/store/apps/details?id=de.dieterthiess.ipwidget)

Get E-Mail Notifications on external IP address changes

Get information about external IP address changes by email.
You need to configure the SMTP connect in order to allow mails to be sent in the background.
Works with Gmail, but requires less secure apps to be allowed. (https://myaccount.google.com/u/1/lesssecureapps)

Just create a separate account if you worry about your data.

After entering the server data, you need to test the settings. If they are ok, you can save these settings and the setup of the plugin is completed.

If you want to monitor your external IP address changes while your device is connected to the same wifi all the time, you need to enable the manual update in IP Widget settings, so the device will update data periodically and will detect changes of the external ip address.