I went through a mild spell of this around a year ago, dizziness, heart palpitations, had three weeks off work with the really bad spells which for me is rare to have any time off work at all. Had all the ECG's etc was referred to a cardio just to be on the safe side as I have private healtcare... all ok.
I was offered counselling but opted for a six month course of citalopram, and am now ok and off medication. The cause of it for me was stress at work, you need to re-train your brain in the way you think about things and situations, for me I have never been a worrier out of work but in work I tended to worry about things too often. There loads of publications about coping with anxiety, but the main thing that I found most helpful was getting up and about and doing things, the dizziness for me was the worst thing to overcome because it was there all the time and never went away, you can and will overcome it.