Here is how to find the public IP address from command line. You first need to install curl as you need to rely on an external web server to get the public IP address. On Debian, Ubuntu or Linux Mint:
$ sudo apt-get install curl
On Fedora, CentOS or RHEL:
$ sudo yum install curl
The following is a list of commands that you can run to determine the public IP address. You can define an alias using one of these commands, or use them in a shell script.
$ curl ifconfig.me
$ curl icanhazip.com
$ curl ident.me
$ curl ipecho.net/plain
$ curl whatismyip.akamai.com
$ curl tnx.nl/ip
$ curl myip.dnsomatic.com
$ curl ip.appspot.com
$ curl ip.telize.com
$ curl curlmyip.com
$ curl -s checkip.dyndns.org | sed 's/.*IP Address: \([0-9\.]*\).*/\1/g'