There is a very general way to solve the problem the two of you are facing. There are seceral services that offer Dyanmic DNS name host services. What these do is give you a name, username.dyndns.org. You run a piece of software on your computer that detects whenever your IP changes, and updates the nameservers. http://www.dyndns.org/
offers this service for free. This lets you not only host a shoutcast station, but also run web servers, or any other server for that matter. The setup is a little complicated, but the Documentation over at DynDNS is very good. I hope this helps.