Seeing double vision with new glasses until I move them up higher a bit?

Eyeglasses. Have your glasses checked to make sure the optical center of the lens is centered over your pupil. If the optical center is not in the proper place it can induce double vision that improves when you shift the position of your glasses.
Optical center. Eye glasses have to be centered on the eye, otherwise they induce a prismatic effect, shifting the image up or down. Check that the lenses are properly centered. The nose or temple pieces may need to be adjusted.