Firstly, congratulations for quitting smoking.
Paradoxically, it is not uncommon for a cough to worsen after giving up cigarettes, but this should settle in a month or so.
Any unexplained cough does need investigating and if you have not already done so, my advice would be for you to seek the attention of your doctor – this is especially so if you are coughing up coloured sputum or blood.
I am sorry that I can’t be of any more help to you at this time, but please let me know how you get on.
Do you have questions? Please feel free to ask.
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