Are you getting any mucus in the cough? I am assuming not since it is a dry cough…
I have been a smoker for the last 12 years and I noticed a ton more coughing earlier during my detox stage. Eventually this normalized.
However, my problem now is mucus plaque forming/causing foods. This includes sunflower seeds, stevia, tea, cigarrettes, etc.
I hope this answers your question. If you are eating foods that are not allowed and notice coughing afterwards, this is because the foods are causing mucus production.
Other than that, I would expect that the cough will go away within weeks.