You should not only do the deep dive course, you should first talk with the instructor and find out very specifically what kind of depths those dives will entail. The standards allow a range of depths (18 meters/go feet to 40 meters/130 feet) to qualify because in a lot of places, there is no access to water deeper than a little beyond the minimum depth range. I know of people who did the entire specialty in a body of water with a maximum depth of 65 feet. I won't do that.
A while ago i was working with a student in a series of advanced recreational classes leading up to the Deep Dive specialty class. A former world class athlete who was still in excellent shape, he was doing extremely well. When we did the deep dive specialty, our first dive was to 100 feet. We noticed that his SAC rate went up a bit. When we did the next dive to about 120 feet, his eyes grew wide, and his breathing rate increased dramatically. I could not believe how fast he went through his air, and neither could he. He was just that anxious about being at that depth, and his reaction was more surprising to him than it was to me. He had assumed he would be fine.
The time to learn that you have some anxiety about going to depths like that is during training. The first time you go to that depth and learn you have a fear of it should not be on a dive when you are acting as a professional leading a group of divers. You should be very comfortable diving to that depth to the point that you can assist with other divers who might be having problems. The people in your charge should not have to be helping you. The only way to be sure you are comfortable diving to those depths is to get enough experience doing it to make sure you are going to be OK.