Do I know if I have a collapsed lung?

Maybe not. Estimated at least 10% spontaneous pneumothorax are asymptomatic. Symptoms if present may include shortness of breath, cough, and/or chest pain. The first line of diagnosis for large pneumothorax is a good history and physical examination (stethoscope). Most smaller pneumothoraces can be diagnosed with good 2 view chest x-ray series. Occasionally, a ct-scan may be necessary.
Generally yes. A collapse of your lung is usually painful and gets worse when you inhale.