I cut my hand with a knife. i took a tetanus shot within 30 mins. however i smoked 3 cigarettes the same day. one 20 mins after the shot. is that okay ?

Smoking by itself does not make a difference in the effectiveness of the shot.. It may kill you from lung disease over time, but it doesn't matter here.

Tetanus toxoid vaccine is administered to prevent any Botulinum spores potentially on the knife to infect you. It does not do anything to heal your laceration or prevent other bacterial or fungal infection. If you have had at least 3 shots including this one in the past 5 years, then you are covered. Please ensure your wound is cleaned and covered.