@anamur-- Did you get a CT scan? That's how they found the foreign growth in my husband's lung that was the cause of his compressive atelectasis.
As far as I understand, compressive atelectasis definition is not always a partly collapsed lung. It could also mean that a part of the lung is not getting much air. If that's the case with you, that might be why your doctor wanted you to improve your breathing. Improper breathing could lead to lack of air in parts of the lung.
Why don't you go back and ask for more details or see another doctor for a second opinion?