Quick throbbing or pulsating horizontal pain across my back?

By quick, I am: assuming you mean brief. Anything that is pulsating would seem to be associated with a blood vessel/heart beating. Hard to know what would be causing pain, but a major blood vessel in the mid-back is the aorta. A problem, bulge/aneurysm, with this vessel would be the most serious cause of your symptoms and deserves urgent evaluation. I would go to ER; this can be excluded easily with imaging.