How soon after quitting smoking will the shortness of breath go away?

Varies: It depends on a lot of things. How long you have been smoking, whether there is a lot of acute inflammation or infection, what the exact factors are in the shortness of breath, are all factors that could influence the result. Unless there has been a lot of irreversible damage to the lungs, you should eventually note improvement. For sure, stopping smoking is your best chance to improve.

Depends: If you haven't done serious damage already (like chronic bronchitis and emphysema), things will improve within a few weeks to a few months. If more damage is done, recovery will be slower and will not be complete. But it won't get worse, which is very important. If you are out of condition, you can help yourself with a gradual aerobic exercise program, which will improve your sob and fitness.