I have a blood clots in my lung and calf of my leg. Am I not allowed to exercise so not to shift the clots upwards?

Only temporarily. In the short term, it is advisable to avoid strenous activity in an effort to prevent movement of the clots. Generally, after you have been on appropriate blood thinners for a reasonable amount of time, your doctor will clear you to participate in normal levels of activity. In fact, as you recover, activity can help reduce your risk of developing swelling in your legs.
Not true. As long as you have been started on blood thinners like Heparin and warfarin then it is advised to walk and avoid lying down with no activity. You should do that with a compression stocking 30-40 mmhg but no strenuous excercise.