Can a menstrual blood clot travel to your heart or lungs like other blood clots can?

NO. Only clots within your circulatory system cause problem. No problem expected with menses, nose bleed, hemorrhoid, cuts, etc.
No. In order for a clot to travel to your heart or lungs, it must be first located within a major vein in the body. Menstrual clots are not contained within hte veins, but within the linig of the uterus, and cannot travel.