I've been getting the same. I'm not used to sleeping on my side and wake with a real intense almost bruise type feeling in my hip on the side I'm laying on. Seems to be worse on the left side. It can hang around for a while in the morning too after I get up. Guess it has something to so with obviously the position and the fact the pelvic bones would be softening in preparation for labour.
I haven't found a solution quite yet but have some nights better than others for no real reason.
Glad to hear I'm not the only one cause I've never heard anyone esle mention this before.

I'll look up with ITB stretch now i think. THanks Georgi