Legend, I gave up smoking last June and for a while (can't remember how long, maybe a couple of months) I felt short of breath. It wasn't a drastic feeling, just a sort of sensation in the background of being a bit short of breath.
Anyway, it went away and I had forgotten about it until I read your post just now. I expect yours will just go away without you even noticing it, but of course, you should mention it to your doctor and they can listen to your lungs, heart and take your blood pressure etc. and reassure you.
Giving up smoking is such a joyful experience. Best wishes