I'm a vegetarian?

You'll probably find that most vegetarians these days will eat fish, milk products, and cheese and eggs. They are what is known as a "uvo-lacto-vegetarian". If someone is more hrdcore than that, thy are often referring to themselves as vegans, which is an entirely different movement again, but those guys won't touch anything tht has been near an animal. So, the safe thing to ask might be "do you eat any animal products at all?" That way, you won't have any uncomfortable moments.