This breathing issue is incredibly common with anxiety, I suffered with it for a couple of years.
There were two things I noticed that caused it.
The first was all over muscle tension. Your diaphragm is a muscle, and if you are tense it doesn't work efficiently. This leads to the feeling of not being able to take a full breath.
The second thing is that in the effort of taking a full breath, you're actually messing up your CO2 levels a bit, effectively hyperventilating. I eventually discovered something called Buteyko breathing. It's completely counter-intuitive, but it teaches you to breathe only through your nose, and not try and breath too deeply. It helps re-balance the O2/CO2 levels in your blood and helps alleviate the feeling that you're always short of breath.
The other thing you must do is stop focusing on your breathing. If you have 99% blood oxygen, you're fine. It's an anxiety symptom.