Very sorry to hear about your issues with anxiety. I sincerely hope you are happy and healthy. 
- Anxiety/Stress Relief
- All Purpose Anxiety Removal
- Pranayama Training
- Lung Restoration
- Become Whole - Self Love
If you can rule out physiological causes for breath impairments, then this may be a good thing!
As for the state of “breathlessness”, that is what we strive for. Breath and thoughts are deeply connected. The Yogic methods tend to regulate and sublimate the thoughts aka the mind through the energy of the breath. This is generally easier (grosser forms of energy are easier to work with).
Others, who practice some direct approaches like some schools of Non-Duality, Advaita, etc., attain the moment of mental clarity and thoughtlessness and their breath naturally slows down and at a stage feels like it has stopped.
I can speak of this in terms of Mantra practice (which is what I am most familiar with) - when the breath seems to stop, it can feel anxious, it can feel scary as breath, in all its glory, is also what anchors us to this physical plane of existence while also serving as a bridge to higher dimensions of wisdom and clarity. So, when this most familiar and intimate process seems to stop, it feels very disconcerting, but that is when old patterns, thousands of years of conditioning begin to unravel. It is only in that state that one is completely undistracted by thought/breath and can see Herself/Himself for what we really are, the Effulgent Radiant Light.
Even during the process of meditation training, we initially focus on breaths, the warmth in and out but once that pattern is stabilized, the goal is to focus on the silence in between the breaths - initially when holding the breath, and eventually when the breath has been exhaled and there is quietness. Eventually when reciting a mantra or meditating, very small periods of such silence begin to appear, where the breath seems to have disappeared. Once the strangeness of this unfamiliar condition is transcended, this state, where breathing has naturally dissolved (this should never be forced) is when the glorious vibration of the Mantra begins to emerge, where every cell in the body begins to vibrate and recite the mantra (mantra’s journey is from gross sound to subtle sound to pure vibration to vibratory intent pre-vibration, then light form and eventually just pure consciousness where the reciter- act of recitation-the mantra, and the deity are one unified consciousness). This state now begins to extend more and more and when one is stabilized in it for a reasonable period of time, it is called Samadhi. This also has the effect of extending the physical life by arresting/reducing the aging process (which is again intricately tied to the breath and its patterns).
Breathlessness is Deathlessness…
