As I understand it, our heads don’t expand, the distance between earth and the sun doesn’t expand, and our galaxy as a whole doesn’t either. That’s because these objects are gravitationally bound. Gravity between these objects is stronger than the force that is driving the expansion of the universe. So it’s the space between astronomically far apart bodies that is expanding, because gravity between these bodies is weakened by the distance to the degree that allows to the expansion force to win over gravity.

Re the other question, yes, red shift can be measured between two points, but they have to be moving in relative to each other. I think that one of the tests that scientists use to determine the speed of space ships is through the red shift effect in the radio waves that is broadcasted back to earth from space ships.