I would cough like crazy every time I quit. The last time I quit, the one that took, I coughed a lot, and just ignored it. Finally after a few weeks I went to the doc, I had pneumonia. I credit the pneumonia with getting me over the hump. I really didn’t feel like smoking at all.
Could just be plain old allergies, though – these days, I don’t smoke much (maybe a pack every week or two), but allergies I didn’t ever have before have me waking up vomiting from the mucus ingested, I suppose, and hacking like a cartoon character.
At any rate, it will pass, even if it is your body getting rid of accumulated inhaled irritants.