I stopped smoking for a week n had been experiencing serious shortness of breath. Upon smoking a few cigarettes I felt my nose clear nsuddenly ok. Y?

Stopping is best. You nasal passages and throat and lungs have had years of serious toxicity from tobacco smoke, they have adapted to this nightmare you are putting them through. You stopped and they had to re-adjust and there will be changes. Be patient because the good to come will far outweigh any temporary adjustment. Get off the cigarettes and stay off.
No idea. But it is common for cough and sputum production to increase after stopping smoking, because your lungs are now able to clean themselves out from the crud you have been putting down there. The coughing can feel like shortness of breath. Don"t start again because of this. You will feel better and better after a few weeks, and the health effects will be the best thing you can do for yourself.