Never bounce when stretching. After warming up, strength exercises can be done with controlled movements. It is OK to feel some burning sensation within the muscle, but you should not have pain. And any burning should go away shortly after completing the exercise. Cardiovascular or aerobic workouts, while stressful, should not be painful.
Any pain is an indication to stop the exercise.
Never try to work through the pain. If the pain persists, you should consult a doctor. And forget the slogan No Pain, No Gain.