its nothing to worry about, anyone who knows your skype or to whom you've ever sent an email can see it, maybe if you have lots of enemies you'll get ddosed but thats about the worst that can happen
who told you ips cant be changed?
Depends on type of connection and company. Some are dynamic and can be changed if you use a different MAC address.
Others are static IP's those cannot be changed by yourself. If you contacted your ISP though they could change it, but it would take something from their side.
Personally I made sure routers did not have default passwords and also turned off telnet and such into my router for the moment. (Granted it is overkill most likely).