To me, it sounds more like some kind of performance anxiety type of issue. A lot of that will go away with experience. As you begin to see the same types of calls over and over, you will find that a lot of your anxiety goes away. It's just because you've seen it over and over again. It becomes no longer new. In a way, it becomes routine. Probably the biggest thing you can do is breathe. Take some long slow and deep breaths when you're called out to a scene. Then actively start relaxing on the way out to it. That way when you get there, you will be calm, relaxed, ready to go to work.
Above all, remember that it is their emergency, not yours. It does not mean that you don't do your best, it just means that you not take personal ownership of their problem.
Way back when, when I was doing my internship, I used to take a nap on the way to calls while riding in the back. I really truly did not fall asleep, it just ended up being about an extra 5 min. or so of relaxation on the way to the call. Because I was an intern, I did not have to concern myself with figuring out where we were or where we needed to go, mostly because we had 4 hospitals within a very short driving distance and I had a pretty good idea where we were relative to those hospitals. That was something I just used to do to keep me calm on the way to calls when I was 1st learning to be a paramedic.
These days, I would probably get some kind of anxiety at 1st if I were to return to ambulance work, but I would expect that to go away fairly quickly as I would settle into the role of paramedic again.