I had real problems with racing heart, I felt like it was leaping around in my chest. I'm obviously in tri 1, though.
DH took me to the doctor and they said that if it's enough to stop of you doing anything, or it's persisting then the advice was to go to A&E, because for the sake of an ECG it's just not worth the risk to not get it checked out. Especially I would say if you already have asthma.