Many chest diseases occur in conjunction with a normal or only slightly abnormal chest x-ray and with a normal bronchoscopy. Lung disease can also occur with normal PFTs, especially in the early stages. The cough, discolored sputum and shortness of breath suggest some type of chronic lung disorder and the CT scan, being more sensitive than a chest x-ray, may allow your doctors to make a diagnosis, and should be done. The 'speckled chest x-ray' suggests a type of lung disease called interstitial lung disease and this is often associated with abnormal oxygen transfer and low oxygen levels.
Ultimately, you may need to have a biopsy of your lungs to make a diagnosis so that specific treatment can then be given.
Thank you for your comments they were helpful .
I forgot to add I am female nearly 50 yrs old and am a smoker.