Unfortunately i've been feeling this way for months. Exactly like you described. I take my bp regularly (it was low during my first and second trimesters), i've had blood tests and everything is normal. My dr just said it's something i have to put up with. Which sucks because i'm pretty wiped out every morning.
There's something called orthostatic intolerance, which isn't uncommon during pregnancy. What it means is that your body doesn't tolerate the changes in blood pressure that naturally occur when you lie down or stand up, and staying upright can be a real trial. Postural hypotension is really common in the mornings when you've been lying down all night, and then gravity has a real go at all that extra blood volume when you are up and moving around. One of the first symptoms for me that I am pregnant is that I can't hold a hair dryer up to do my hair because it makes me faint!!