It sounds as though your "home setup" DNS servers might still be pointing to the old site. If the site you see at home has the "same" pages as the last version you had at the old webhost, I strongly suspect this is the problem.
How to remedy the problem depends upon who your ISP at home is, and how you specify which nameservers to use. It actually can get even more complicated if your home system "caches" DNS, and we would need to know more about how your home system is set-up to help.
As you might (justifyably!) might be reticent to share those details in a public forum, I suggest you contact the Customer Service department of your home ISP (I know that sounds painful!) and explain the problem to them exactly as you explained it here. After they get done putting you through the hoops of "clearing you cache" and "closing/restarting your browser", and all the other "script-based" stuff they always seem to have to have you do, they should get to the DNS issue.
If you want to be really prepared for that call, you might run a few reverse DNS lookups from Home and at Work to see what you find, or use other net tools to identify which ip address your pages are being served from at each location. This ought to help the tech guys understand what is happening.
Good luck, and let us know what you find out.