Some of the symptoms you list are not part of an anxiety disorder. Having a fast beating heart when you are running is completely normal; your heart rate is supposed to increase so that blood circulation, and thus oxygen circulation throughout the body is increased. If it is going over your target heart rate (you can find online calculators to determine what this ought to be) by very much and staying there then you have something besides an anxiety disorder going on.

Because your heart rate escalates so quickly with the slightest bit of exercise, it more sounds like you're really out of shape. People who normally lead a sedentary life can become winded and have a fast heart rate just from bending over to tie their shoes. Being out of shape this severely can also cause bodily tremors as the muscles become fatigued very quickly and have trouble supporting normal activities.

I think you need to try exercising more. Exercise is good for helping to control anxiety disorders and will also train and tone your heart, lungs and muscles to be able to handle whatever kind of stress you're putting on them. Yoga is a great body toner and can be done at a slow pace so you don't feel the need to quit once your heart gets pumping all of the sudden. Then you'll want to advance on to other more aerobic exercises like slow jogging, not running, and increase the speed from there.