I had this happen with all my pregnancies. FWIW, it's worst in the first half of the pregnancy, for me-- in the second half, and especially in the third trimester, it seemed to ease up a alot. I think though that I was also much less active in the second half, so maybe I noticed it less.
If you're worried, I would encourage you to see a cardiologist at an office visit. It was very reassuring for me-- the doc was able to send me home with a little monitor to track my heart for 24 hours, and then I went back and we looked at it on a computer, to see the patterns- was the average rate within normal limits? What activities seemed to trigger the symptoms? What times of day? She spent more time with me than ER docs typically do, and helped me to worry less about it.
me , he , my three , , and -- and the one we lost