as a smoker when you light up a cigarette you take a DEEP breath to pull the smoke into your lungs. When you stop smoking, you stop doing that large inhale, and you no longer exercise your lungs in the same way. the diaphram which is used to expanding several times an hour now lays around.
Some folks fall into a pattern of sighs some deeply after they quit, some cough. It sounds like your lungs are finding a way to adjust to their new life.
Practice deep breathing! yoga breathing. stand tall, draw in air. Expand those lungs. move that diaphram. dont let it get lazy. This time, you are drawing in good O2 and fresh air. I think you will find in the next few weeks that passes.
Just keep breathing! as those little hairs (cilia) grows back on the lining of your nose, lungs, and airway it will start to retrain them selves for what they do naturally.
Im so proud of you!