Do you know if you clench your jaw or grind your teeth in your sleep? Usually either you or your dentist will be able to tell due to chips, cracks, and/or excessive wear.
I do both, and I wake up with the type of pain that you're describing frequently. Your jaw muscles are huge, and it's strange how the pain can radiate along the sides of your head. Sometimes I only get pain on one side, sometimes it's behind my eye(s)-- it's really unusual.
We anxiety sufferers are well acquainted with stress, so this may be some stress-induced jaw clenching.
You could try to put a warm compress on the side of your face and see if that eases the discomfort.