If you uploaded your site with an IP address, chances are others are already seeing your site on the new host.
If you still aren't able to access the site on the new host, perhaps a call to your ISP will get them to do it quicker ;) Many ISPs will update nightly, or every other night, although there are a few out there (such as mine) that don't find it nearly as important to update as frequently. However, since my complaint, they seem to be doing it nightly or at least every other night now.