I have been looking through a looooooooooot of designs lately. And a lot of them aren't entirely original. About 10% of the submissions seem to have a link somewhere in the comments to another design very close to it. Cries of plagiarism are hurled back and forth.
But most of it isn't plagiarism. (Though granted, some of it is.) Some of these ideas just occur to multiple people at the same time. Whatever muse there is of t-shirt design, she's got so many people trying to come up with ideas, that she thinks she can just hand out the same idea to lots of people and maybe no one will notice.
But the great thing about the internet is that there're search engines all over the place. Do a little research. See if your design has been done before. (Or at least, if it's been done before, it's only been done a couple times, and in different ways than your idea, rather than a hundred times with every variation possible.)
You'd be surprised how many original ideas are out there. You still might not get printed, but at least you'll know you did something you're proud of, and that not everybody in the world already thought of.