Drastic - 1:57 am on Jun 19, 2001 (gmt 0) Welcome to the forums, BTW.
Just to be sure, type the IP into the browser address bar, and refresh it a few times. If no other site ever shows, you should be on a dedicated IP. That doesn't mean your host won't share it in the future, however. To find out for sure, just email your host, and ask if your site is hosted on a dedicated or shared IP. That should clarify it for you, for future reference.
Welcome to the forums, BTW.