First off, I do not agree with the other responses in saying it was rude of the daycare worker to ask if you smoke.
I am extremely allergic to cigarette smoke, second hand cigarette smoke, and cigarette smoke that becomes permanently glued or attached to my clothes from being around places where people smoke. I have had to throw away clothes because airing them out and washing them still does not get rid of that particular smell.
I actually get migraines from cigarette smoke and my eyes begin to itch. Both of these will last for a couple to three days for me. It is rather debilitating.
If your daycare provider is asking, she sounds like she has a very sensitive nose and is trying to figure out what that particular smell is. So I understand her question.
If you call you a professional or industrial cleaning services that specializes in cleaning homes after fires and floods, there is a 'bomb' that actually targets the cigarette smoke molecule and changes the smell forever. It works quite well.