Are you feeling as if you're going to kill over?
I have the same type of anxiety that way like I'm going to get a heart attack when I'm being very vigorious cardio-wise.
It's common to think that an increased heart rate would trigger and release the same signals from the brain as if fight or flight was kicking in, and I can see where that increases our anxiety.
There are far more exercises that can release the stress and tension that anxiety causes and gives you a more.... open mind to things per se.
If you're an avid runner, you've gotta keep in mind that you're not going to kill over, and if anything were to happen (you passing out) you've got a bunch of people around you (in a gym) that would be there to help you.
I mean I don't know if you're running outside or indoors at a gym, but if you're at a gym, increase your speed until you start to feel the panic and on the treadmill or eliptical or whatever you're on almost EVERY machine is equipped with a heart rate monitor. Count your pulse... if you get high and uncomfortable, slow yourself down until you're in a target area and kick it up again... If you do it a few times you'll be able to do it 100 times.
I always rely on that heart rate monitor to physically convince myself that my heart isn't at a 200+ pulse. when in all reality it's at like 150-160.
Just take some breaks to cool your senses and hit it again, I know it's hard to be running, and stop running and then trying to start up again, but if you're trying to run a few miles with the entire mindset of increased anxiety, you're not going to perform as well and your body is going to try and counter-act what you're doing.