What does it mean if smoking a cigarette calms me down? addiction?

Probably .: The calming effect of nicotine may be caused by the increased release of neurotransmitter a in the brain, especially, dopamine. Dopamine then acts on the reward system to create happiness, euphoria and a calming feeling. An addict can get very agitated and anxious about getting their "fix". When that "fix", or drug, or drink is obtained, the resulting reduction of anxiety is perceived as a calm.