If you are using Arch Linux feel free to use this AUR.
https://aur.archlinux.org/packages/gnome-shell-extension-public-ip-git/
git clone https://aur.archlinux.org/gnome-shell-extension-public-ip-git.git
cd gnome-shell-extension-public-ip-git
makepkg -sri
You can download extension from link above.
Or install manually (but if you already use site for another extensions, then disable autoupdate)
If you want install it manually, clone project to ~/.local/share/gnome-shell/extensions/public-ip-extension@rostegg.github.com folder and restart gnome desktop (Alt + F2 -> r -> Enter):
git clone https://github.com/rostegg/public-ip-gnome-extension.git ~/.local/share/gnome-shell/extensions/public-ip-extension@rostegg.github.com
This may be for two reasons:
If you want to add own service, just create issue with link to api.
For bug report provide gnome shell version (gnome-shell --version) and error message, if installation failed (Alt+F2 -> lg -> Extensions -> Show Errors).