I have found that when I am really anxious I stop breathing. When you stop breathing all kinds of strange physical things start to happen. If you want, try this experiment: When you are feeling really anxious (hopefully at home or in your car at the time) SING really loudly. I sing old Slavonic church songs personally. You will feel and sound ridiculous but see if you don't feel better immediately afterwards. I think its the breath control and the switch of focus from the anxiety.
I did this alot when I was having anxiety while driving. When I'm really freaking out I lose the feeling in my arms, hands and legs. Not too great while driving! Still today, like if I have to pass directly between two large trucks that going 80 mph I will belt out a rousing version of something or other.
In the very least, I think this might help you to understand that you are not crazy and that these feelings really can be made to go away.