Whoops. I'd say that you made a good faith effort, so you shouldn't feel too bad about calling yourself vegetarian. However, if being a vegetarian is important to you, it makes no sense for you to eat gelatin.
I suggest thinking of it as any other "hidden" ingredient. Let's say your grandma makes you some nice vegetable soup. Later, you realize she put in a chicken bouillon cube. It's obviously not vegetarian, but because you didn't know, I think you get a pass. However, if you go out and order a big bowl of chicken pho, you are knowingly and intentionally eating something non-vegetarian, so it really is dishonest to say that you are a vegetarian.
Aside from gelatin watch out for animal rennet and junket. Both are slaughter products. They're basically digestive enzymes that function as coagulants. (I know, that sounds nasty.) You'll usually find them in cheese. Check the label or look up the brand online. Google "joyous living cheese" for a list of cheeses that are (or aren't) vegetarian. Junket is used in custards and puddings.
Beyond that, watch out for fishy stuff. Worcestershire sauce, for instance, is made out of anchovy. Caesar dressing usually is as well. Many Asian sauces will contain fish sauce or broth (dashi does, ponzu usually does, teriyaki might). Thai-style curry sauce might contain dried shrimp.
You should also double-check the labels on your cheesecake ingredients. Full-fat dairy products are usually gelatin-free. (The gelatin is used as a stabilizer and texture agent when they remove fat.) You might be safe.
Good luck!