The shortness of breath is pretty normal as bubs takes up more space. I'm like you and am short with a short torso so I noticed this with both pregnancies.

I think I know what you mean with your heart racing - I used to get it when I took ventolin. I can't recall if I had it in pregnancy but it does sound like it could be anxiety related. I did the hypnobirthing course and found that it was really helpful in enabling me to adjust my breathing to control my heart rate. This might be worth looking into to help control it if it is anxiety related.