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Hello and thank you for the question.Answers given are for informational purposes only and are not meant to replace an exam by an in-person.I am Dr. Sohaib, a practicing Internal Medicine Specialist and I will do my best to help you today.
Usually when the chronic smokers stop smoking, the cough becomes little more severe and productive because the damaged epithelial lining of respiratory tract due to smoking, starts regenerating.
However, since it is only your throat, this doesn't explains the cessation effect of smoking satisfactorily.
Chronic smokers usually have some cough, so when they stop smoking the cough becomes more initially paradoxically due to mechanism I explained earlier. Productive means cough with phlegm.
Usually this kind of throat irritation is secondarily to allergies (environmental) or gastroesophageal reflux.
Since you have been smoking, there is most likely an allergic response or reflux from stomach
Because in the absence of fever this prolonged symptom doesn't look like to be due to infection.
Now with 3 weeks history of these symptoms I would suggest to have this evaluated by your doctor, and not to wait any further.
There is no harm to continue with lozenges; but this is giving you a temporary relief only and the cough is still persistent; We need to identify the reason for that and treat effectively; that's why you need to have this evaluated Soon.
I would do a chest xray and some basic blood tests like a cbc initially. And if nothing found may be you need an endoscopy to look for reflux.
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