Can hypertrophic cardiomyopathy cause chest pain or tightness?

Yes indeed: If you are sure you have hypertrophic cardiomyopathy (it's a completely different animal from an athlete's hypertrophy), then you need to hustle to your cardiologist. I am not kidding. There may be obstruction to the outflow of the left ventricles that will interfere particularly with filling of the coronary arteries. Or it may be nothing. But get seen.

Yes: Hypertrophic cardiomyopathy can cause chest pain. It is a condition in which the heart muscle becomes thick, and obstruction to outflow may occur. Arrhythmias may occur as well. Patients may have severe symptoms, or no symptoms. It is a common cause of death in young athletes who seemed completely healthy.