Yep, certainly sounds like panic attacks to me. Good for you to get yourself checked out medically to rule out anything else.
Anxiety feeds on itself, the fear of the feelings of anxiety feeding more fear, and therefore more anxiety. And so on. Its important to know that you are NOT having a heart attack or going to die, and that the feelings WILL pass...but being able to hang onto those thoughts in the midst of an attack is understandably almost impossible.
I believe its not unusual for this to overtime develop into agoraphobia or panic attacks.
I can recommend Claire Weekes 'Self Help For Your Nerves' book, where she explains each and every symptom of anxiety and panic, and discusses really helpful ways to deal with it (as well as breathing exercises as the previous post suggests), such as imagining youself floating above the anxiety (a sort of dissociation technique, which allows you to take yourself away from the immediate feelings and observe what is going on with a more objective viewpoint).
Also, there is an excellent FREE step-by-step CBT based programme online, called 'Living Life To The Full' by a doctor Chris Williams who is a recognised expert in the field here in the UK. It has whole sections on anxiety and related symptoms, and you can work through it as a self-help course.

Hope that helps, and I really hope you feel things turning around soon,

Best Wishes,

MattC