What is the right test for my research question?

My research questions is what is the likelihood of a patient having a specified medical complication who is a smoker compared to a non smoker? I have calculated the proportions in each relevant group. I would like to analyse each specific complications i.e. pneumonia, reintubation, renal failure etc and so on as per table below.

I have been told that a binomial logistics regression analysis is what I need to do. I wanted to check this is correct and secondly to check that I am doing the analysis correctly. See table below