If you have a router, it will almost always allocate each of your PCs (even if there is only one) a separate IP address from your “external” IP address. This address will usually be in the form 10.*.*.*; 192.168.*.*; or 172.16-31.*.*. These addresses are free for anyone to use on their home network (and the same address can be used on different networks) but can never be used on the internet. As a result the router has to perform some magic (Network Address Translation, or NAT) which inspects all the data your PCs transfer to/from the internet and “translates” your internal address(es) to the external address on the way out, then when a reply arrives (sent to your “external” address) it remembers which PC made that connection and translates the address back.
To find this address you can (at least on windows XP) go to Start → Run and enter “cmd”. Then enter “ipconfig”. One of the lines which appears should list “IP Address” in one of the forms listed above (10.*.*.*; 192.168.*.*; or 172.16-32.*.*). This is your “internal” address. If the IP address listed is not in one of the above forms, but matches the IP address from “myipaddress.com” you should be able to use that address directly - but you will still need to ensure the appropriate port is allowed to pass through your firewall.
If you cannot find your internal IP address in this way, you will again need to check your router settings. This time you are looking for an “internal”, “LAN” or “local” address. If you have multiple computers connected to your router, you will need to be sure to pick the address of the one you intend to run SimSig on!