Your question is very brief, but the short answer is it depends upon the contractual terms you entered into when you designed your t-shirt on that other site. In my experience, most design sites make themselves available in order to attract designers just like you. Their ultimate purpose, however, is to have you and all those who would like to buy your designed T-shirts from THEIR SITE. That's why they put their time and effort into establishing their web site and allow it to be "free", although that's also why its not actually free. They want to charge you every time you order that design for one of "their" shirts.
If you take the design and move it to your own site, you may be violating one of their contractual rules and/or the copyright on the design, which you may have inadvertantly given away when you designed it on their site.
