Hi EM.,
Yep, the Cortisol is a stress hormone, and like adrenaline, can cause residual symptoms like you described. Cortisol helps us to get up and go after sleeping all night, so it is by nature, stimulating. Unfortunately, it is often to much for the anxiety sufferer!
Exercise can help to burn off this effect. Of course when you are feeling awful, it can feel impossible to get going with any activity.
Therefore, if you can try to get in a calm state with some of the coping skills I will post below...and then use your exercise as a secondary defense against the anxiety...I am pretty sure you will see it lessening in time.:)
Self Help sites with breathing/relaxation exercises instructions
Panic attack relief exercises:
http://www.healthcentral.com/anxiety/c/73076/34334/breathing-lessons/
http://www.healthyplace.com/
http://www.stress-relief-exercises.com/
http://www.ehow.com/video_4405003_breathing-exercises-panic-attacks.html
http://www.psybersquare.com/anxiety/panic_relax_I
Best wishes and keep posting!
S.C.