No, you're not a vegetarian. Vegetarians do not eat animals. Fish are animals.
I love sushi too, but then again all sushi is is just cooked rice rolled in seaweed sheets, with thin strips of something in the middle. In my case, being a vegetarian, the thin strips are strips of carrot, avocado, cucumber and things like that. A dash of soy sauce and a smear of wasabi, and Bob's your uncle!
Eat fish if you want to, but don't then call yourself a vegetarian. It spoils things for the real vegetarians.