The calcifications you describe are of little or no consequence. In the huge majority of instances, they are indeed a reflection of prior infection, with either fungal infection or infection with the bacterium that causes Tuberculosis. Such calcification are common. They are an indicator of healing and, for the most part, pose no risk of recurrence of the original infection. In either instance, these calcifications pose no threat to you or to your lung function. They are not associated with cigarette smoking or with asthma.
That you “frequently suffer from cold and cough” is not normal. You and your doctors should strive to find the cause of that and treat it, but these episodes should be seen as unrelated to the calcifications.