Yeah, it can wear you down, especially if you get caught in a cycle of trying to catch a deep enough breath through-out the day, which in turn leaRAB to hyperventilation syndrome. The constant exercise of trying to breathe deeply ENOUGH can make you feel exhausted, particularily if you are like me and that "breathless" sensation starts the moment you wake up in the morning. I've been dealing with this since 2008.
My upper body (shoulders, neck, and chest) are usually tight and feel heavy because of this. It's not due to Asthma so I've been told, but it's caused by reflux. Have you been diagnosed with LPR?