This is me exactly. I slept on my back, and since I've been sleeping on my side, I wake up with hip pain that radiates down my legs. I tried the pillow between my legs and that didn't help. The only thing that has helped me some is wedging a huge pillow under half of me so I can kind of lay on my back but I'm still tilted to the side... that way all my weight isn't on my hip. I do the same thing when I flip over... wedge the pillow under my stomach and sort of sleep half on my stomach, half on my side propped up by the pillow. That has definitely helped.
I told my OB about my hip pain yesterday at my appointment, and she said it sounds like sciatic nerve pain. She suggested that I see a chiropractor. Haven't decided if I'm actually going to do that or not... But if the pain gets worse, it's worth a shot!