Do you have any literature about your fireplace or any memory of whether it is vented or unvented? If it is unvented, it could very well smell. The smell of natural gas burning is something I can certainly smell, and it makes me feel tight in my chest. But I have asthma.

If you have an unvented gas fireplace, you need to learn a lot more about the dangers of one. If you go to the first page of the Fireplaces forum, where the titles of the posts are listed, you can scroll down and find a search box. Do a search on "unvented" and you will learn a lot of life-and-death info you really need to know. It seems that simply stacking the ceramic logs wrong in one of these can cause it to burn wrong. That could deplete you oxygen or put carbon monoxide (which has no smell) in your air. If your builder or previous owner did not leave you a manual on the thing and you cannot find a make and model number so you can find the manual online, I would not use it at all.

If you have a gas log set in a real masonry fireplace, did you make sure the flue was open before you turned the fire on?

If you have a sealed-in-glass gas insert that is directly vented through the wall behind it or through a chimney, you should not be able to smell anything.