Question about IP address

[DAILYHUNDRED]

Ok so I figured out how to change my IP address. I just unplug my modem and router for 30 seconds. I then go to IPBurger.com and it works the ip does change, but when I go to run>cmd>ipconfig/all the ip address shown there is different from the ip IPBurger gives me. Also the ip shown does not change stays the same. Is it ok to log into accounts as long as the IPBurger ip changes. I'm worried they might link me since the ip shown doesn't change run>cmd>ipconfig/all. Does this happen to others too or is just me? Thanks

[GreenBean]

Always better to say what gear you are using so the advice is accurate

[DAILYHUNDRED]

I'm using linksys G Router & Motorola modem. I use AT&T as my DSL provider, Thanks