Your points are alright, however, it can be better if you could polish your essay to a more objective one even though the question is inquiring for your own view.
For example :
Furthermore, if the authorities ban smoking in public places, smokers will say this is discrimination against them.
It would be better this way "Furthermore, if the authorities ban smoking in public places, some smokers would regard this as a discrimination against them."
Not all smokers will be annoyed by the authorities, for sure. So, it would be better if you write "some smokers". Besides, "will" should be replaced by "would" to make it less stronger (because not all smokers will complain).
Using "say" will make your essay sounds less academic, so it is better to be replaced with "regard".
You could also consider to not use a very complex sentence because it will just make the readers confused.
In my opinion, smoking must be banned in public places, because other than causing health problems to themselves as smokers, they also affect non-smokers' health, especially children's and infants' who inhale cigarette smoke, which is very bad at such an early stage of their lives.
It would sound better like this :
In my opinion, smoking must be banned in public places. It is because other than causing health problems to themselves as smokers, they also affect non-smokers' health, especially children's and infants' who inhale cigarette smoke, which is very bad at such an early stage of their lives.
Moreover, you should provide some examples of health problems like perhaps lung cancer. It will make your statement stronger by providing proofs.
Overall, it is a nice essay. Keep on writing !