Does your body naturally produce nicotine?

No: There are "nicotinic receptors" the actual chemical that binds there is usually acetylcholine or other similar compounds... Not nicotine, which is a neurotoxin.

Nicotine: The human body does not produce nicotine. However, the body does have nicotine receptors to which when introduced, nicotine binds and produces it's effects. In order to have an effect, most drugs that work on the central nervous system need to attach themselves to a specific receptors in the body.