From my point of view- you are counted as Puerto Rican. If your parents were born and raised in Puerto Rico, or even if they were raised somewhere else, but still with the knowledge of Puerto Rico, you are considered Puerto Rican. Take for example, Jennifer Lopez. Her parents are 100% Puerto Rican, and JLo was born and raised in New York. She is still considered Puerto Rican, because she says that she is, and she feels pride in it.
Most importantly, to say that you really are Puerto Rican, you answer it yourself. If you feel like you are Puerto Rican, then you are. If you don't, you're not, even though you know that you are.