That's the way my anxiety is too. I'm calm and cool when I'm busy, busy, busy at work. Other people get stressed out, but people are always amazed by how focused and calm I am in those situations. When I went to do a live interview with the lead singer of my favourite band, my friend (and interview partner) was freaking out before he showed up, but I was calm, cool, and collected. I'm usually like that in situations most people would find stressful. Job interviews, for instance, don't bother me at all.
My anxiety sneaks up on me when I'm NOT busy and NOT under any immediate pressure. Once I got over agoraphobia and went back to work, I didn't have panic attacks when things were stressful at work. Instead, I had panic attacks when I was alone in my office or on the bus and my mind started to wander.
I'm still trying to LEARN how to relax... because it gets exhausting trying to keep myself busy all the time to keep the anxiety at bay. I use distraction techniques to keep my mind occupied when I'm trying to fall asleep... so I won't panic. I hope that someday I'll get to a point where I can just BE rather than always trying to keep my mind busy.
I'm SO much better than I used to be, though. CBT and meds helped a lot. I'm really glad I got past the denial and got some help. I hope you can do the same.