I get the same thing, actually sometimes it happens to me while laying down doing nothing. My doctor said it's probably the baby putting pressure on a nerve (i think he said nerve?) that runs to your brain, which is why you may get dizzy or lightheaded. The short of breath comes from there being no more room for your organs inside and everything gets squished up until your ribcage and puts pressure on your lungs.
So fun though, huh?? I get it all the time... and have a very un-understanding household! (a 2yo and a fiance who thinks the only hard part of pregnancy is carrying an xtra 30lbs, which he "does every day, just in the form of a toolbelt, not a baby").