I've been feeling very lightheaded, is this normal? 37 weeks in 3 days.

Almost there. Yes, it may be normal at times for you to feel lightheaded, may sure that you are keeping hydrated and eating well. However if you have been told that you were anemic ( low blood count) this pregnancy , i would confirm that you are taking your iron supplements. Also check blood pressures, if the top number is less than 140s and the bottom number is less than 90s, then just talk with your doc.
Lightheaded and preg. Not unusual as fluids shift during this part of the pregnancy. I would keep yourself well hydrated with fluids and if the lightheadedness continues - check with your OB - you may be anemic .