I actually had this same problem, but was able to overcome it using a sort of exposure method. I started by taking slow walks around my neighborhood (strolling, not exercising) every evening. I did this for a few days so that I got real comfortable. Then, once I got within sight of my house at the end of my walk I started picking up my pace. It made me uncomfortable, but I knew I only had to go just a short way until I got home, and it would be ok. As I got used to that, I started the faster pace earlier in my route until eventually I was power walking all the way. Then I repeated the process by adding running to the last little bit and increasing that distance slowly until I was running the whole way. From there I gradually increased the distance of my overall route. All in all it took about a month - maybe a little longer. I still had occasional panic attacks, but I would force myself to finish as planned anyways. Now I hardly ever have panic attacks while running.
