The lungs generally take the longest to get better. They're constantly flexing without stop, so it's a slower process to repair.

I'm saying this from experience as someone who has asthma, allergies, and had a cold or bronchitis an average of once every four months or so growing up. It can easily take several months for a general cough to go away.

Don't take any of this as medical advice, but if it's not getting better (or if it gets worse), you should go get it checked out.