Shortness of breath and a dry cough for an extended period of time warrants a visit to your primary doctor
or a pulmonologist
(a lung specialist).
As for your specific question, Interstitial Lung Disease (or ILD) is a group of disorders that involve the lungs. It is not one specific disease, but a category. The word interstitial refers to the fact there is abnormality in the lung tissue itself and not the surrounding structures. While classically the disease cause alteration of the alveoli (or the part of the lung where gas is exchanged), there can also be changes that occur in the airways. We group these disorder together as they have similar clinical, radiographic (on x-ray or cat scan) and pathological mechanisms.
The group of ILD are divided into those that have known causes and those that are idiopathic (in other words we don't know why they occur). Some known causes include pneumonia (infection from bacteria, fungi or viruses), exposures (like asbestosis or coal) and auto-immune disease (lupus or rheumatoid arthritis
People with ILD may have shortness of breath and cough. The true way to make a diagnosis is to see your doctor so that he or she can evaluate for possible causes. An x-ray and lung function testing may be needed. If you are concerned you may have this, seeing your doctor soon can be helpful as some ILD causes are better treated earlier before they permanently damage the lung.