After the baby engages in your pelvic area, this breathless experience will lighten. Yah, right!? I actually found that getting up and walking helps, it takes the baby's pressure off your chest area. Also sitting straight up can help. It will get better!! :-) Drink cold water and try laying down on your left side, you will get a better oxygen flow. Also even sometimes sitting straight up and leaning forward and breathing in slowly as you move back and forth (rocking) also does magic!
I thought I was the only 1 that gets this but most of the times I jus have to sit for a while because if I dont I will start to feel like im going to pass out