How to track my public IP address in a log file?

I'd like to save my public IP address to a log file so I can use them to exclude my own visit to my websites in the stats collections. At the moment I can see my actual public IP address-- but I believe that every time I off the modem, it changes.

I don't have a static public IP address, and I think there isn't a fixed range of IP that my ISP is giving me.

I'm running Linux Mint 17.3, is there any way that I've already a similar log file? If not, can I track my future IPs and how?