I totally understand what you mean. One thing you can learn to do is to try to get your body to breathe with your belly as opposed to using your chest. One of the first things that helped me in the beginning was to do this exercise where I would lay down, place one hand on my chest and one on my belly, and focus on making sure the hand on the belly was moving up and down rather than the hand on the chest and try to focus on belly breathing as much as possible throughout the day.

I also dealt with the deep breath issue where whenever I would take one in, it wouldn't always satisfy the "hunger" for air and leave me with an empty lungs feeling even though my heart rate and breathing rate were normal. The feeling isn't as bad now as it was then when it started as I've learned to manage the issue with breathing exercise and moderate physical exercise while belly and nasal breathing.

Have you thought of ways to deal with the potential anxiety and stress, such as any relaxation techniques?