Whenever you notice your body getting anxious, here's another simple self-soothing technique you can use to calm yourself down.
I call it The Fingertip Squeeze. All you do is squeeze the tip of each finger while you take in a slow, full breath and then slowly let it out.
Using your thumb and forefinger, simply squeeze each finger of the other hand from side to side near the tip. If you feel up and down the fingertip area, you'll notice that there's a little dip on each side, about even with the base of the fingernail, and that squeezing there just feels right somehow. Do each finger and the thumb, with a long, slow inhale and exhale while you squeeze and hold each one. You may want to stay for more than one breath before moving on to the next finger. After doing one hand, switch and do the other hand. As you move slowly from finger to finger, you'll notice your entire body slowing and calming down and your breath slowing and deepening.
The Fingertip Squeeze has the advantage of being discrete. If you leave your hands in your lap while you do it, no one will notice. While sitting around a conference table during a business meeting, you can do it under the table, completely out of sight. While sitting in the dentist's chair, you can do it in your lap. You can do it almost anywhere, without anyone noticing and without attracting attention to yourself. Again, remember to breathe.
In the longer term, you can also create more self-confidence and inner strength by literally creating a stronger felt-sense of self in the core of your torso, but that's a bigger project, requiring months of practice, so for right now, use the fingertip squeeze to soothe yourself any time you need it.
For more info on how to develop a felt sense of your Core go here.