I had something similar while pregnant, for me it was anxiety attacks. Are you more stressed then normal? Once in a blue moon I would get an anxiety attack before I was pregnant, I got them a lot more while pregnant (working two jobs, trying to get ready for the baby), but after my pregnancy I rarely get them. The more you worry about the fast heart rate and shortness of breath the worse it gets. Take deep breaths, relax and continue this till you feel calm and gain back regular breathing. Mention this when/if you talk to a doctor, they would be able to give you some tips, I do not remember them all.
http://www.cafemom.com/answers/217990/33_weeks_pregnant_R...
Another source says that is has to with having more blood since you are growing a little one inside of you. Plus you are using more energy to grow that little one so an activity you do could leave you without breath or winded.
http://www.medhelp.org/posts/Heart-Disease/fast-heart-rat...
Here is something someone else posted a few years ago, so take it with a grain of salt: I had that when I was pregnant with my first son, and even worse with my second. Nobody could help me though. Four years later I found out that I have PCOS which is cysts in my ovaries, and it comes along with many other horrible symptoms. I also have insulin resistance. With this it happens mostly right after a meal. I have a rapid heart beat, I feel weak, and I am totally fatigued for a good hour. This happened while I was pregnant, and now after. I gained way to much weight with my kids, and had them 14 months apart so the pregnancy was very close together. I had severe pain under my breasts where it would burn, and that is also a symptom, you get a hot spot, and the skin gets dry, and there is skin discoloration. I often complained that my pelvic bone was killing me, and it hurt so badly the whole 9 months. They did tests, but were just positive that it was nothing.
When you visit the doc/OBGYN next just ask about the above, and they will be able to sort through the finer details.