Carbon monoxide danger with gas fireplace??

I have a gas fireplace. The flue was shut for 1/2 an hour with it on, when I noticed that it was giving off the smell of natural gas. My parents aren't worried, however I think that there must be some problem. The closed the flue. I did not smell "soot" or any such thing as they insist. It was natural gas. I think I'm getting a headache, although I may be paranoid...Shouldn't I be worried about carbon monoxide?