You can try waiting a little longer. Say 10-15 minutes and see if it makes any difference.
I don't know if you have cable, DSL or FIOS.
There are a set of IP addresses which are called private. They are explained here. Private network - Wikipedia, the free encyclopedia
Since there are not enough IP addresses to go around, a system has been developed toshare a public IP address.
Your private IP address likely begins with 192.168.
Now the tricky part. Within your network at home, all the IP addresses begin with 192.168 and so might your neighbors and so do many other people. It's common to assign an IP address of 192.168.0.1 to the router.
Addresses within your network can be dynamically or static. Static address are best used for printers, servers and access points. Dynamic addresses have a lease time assigned to them. When that time expires, it's likely that a new IP address will be assigned.
A laptop might be best served with a dynamic IP address because it can be used in a hotspot or home without any configuration changes.
If you wanted to run a webserver at home, you'd have to use the services of say DynDNS: Dynamic DNS, E-Mail Delivery and Other Services
and run a program in your router or on another machine that will update the DNS (Dynamic Name Server) system at dyndns.org so that something like myhome. Dyndns. Org points to the address that whatismyip sees. Spaces added intentionally.
Furthermore, you have to tell your router what machine will respond to a "service". A "service" has what's called a default port associated with it. Port 80 is the default http or a web server which uses the HyperText Transfer Protocol
The router will then forward all incoming requests to port 80 on whatever static IP address you specified. A protocol can run on any port. Server and Client have to agree on which one.
On outgoing requests NAT or (Network Address Translation) within the router takes care of the re-routing of requests.
Every interface has a unique MAC address or (Media Access Control). It can be thought of as serial number. That's what makes every connection unique. The IP address is used for routing or where is this message supposed to go just like a telephone number. The telephone number is comprized of a country code, area code, exchange and a 4 digit "extension". That 4 digit extension. Telco wires are just that wires. Those wires need to be assigned to a particular SLI or Subscriber Line Interface that controls your phone.
Now your more confused, right?