Does your chest feel tight & as if you can't get a deep enough breath?
Never heard that it was called "dysfunctional breathing" but I do know that it is virtually universal to all anxious people, including moi :)
Breathing is an odd thing. We feel like we're in control of it, but actually we aren't. You can slow down & speed up your breathing if you want to (and even stop it for a short time) but your brain simply won't allow you to do yourself any damage, no matter how hard you try.
When we're anxious we get into a cycle of trying to control our bodies and find ourselves paying attention to things we've never paid any mind to before - our breathing patterns, heartbeat, even things like swallowing. And because we're paying such close attention, things start to feel laboured and difficult. That's what's happening with your breathing.
I don't like your doctor calling your breathing "dysfunctional" because that implies there's something wrong with it - there isn't. You are breathing normally. You are getting in enough oxygen & expelling whatever it is that is expelled. Your breathing is fine - believe me, you'd know it if it wasn't.
What is dysfunctional is your thought patterns and that's what needs to change. Knowledge is power in these situations. You need to learn and understand that no matter how uncomfortable, nothing physiologically dangerous is happening to you. Once you fully understand and accept that, you can start to let go of those fears that grip you and all of a sudden a day will pass and you'll notice that you didn't think about your breathing once.
For me, understanding panic was the key to eliminating it. I never took any meds, although I know other people have been helped by them. I still get that laboured breathing feeling sometimes, and can feel myself slipping down that slope into panic, but I know that it's just a feeling & can't hurt me, and it loosens it's grip almost immediately.
There are some great websites devoted to panic disorder (and all of them talk about the breathing issue) which have helped me a great deal in the past.
It's horrible what you're going through, but it can be beaten, I promise. Knowledge & understanding really is the key.
Good luck :)