Besides the meds, grounding techniques work very well for me when I feel a panic attack coming on.
I feel that tightness in my chest that signals incoming panic attack, and I stop what I'm doing, stop whatever I'm thinking about. I start to take notice of my surroundings.
The texture of my pants under my fingers. The feeling on my thighs as I rub my fingers on my pants. The quality of the light in the room. The play of the shadows. Whether it's tactile, visual, smell, auditory, taste, or just consciousness of your thoughts, it's about interrupting the attack before it takes hold. Distracting yourself with mindfulness of your surroundings stops the feedback loop that creates the panic attack.
It's like when a scratched record keeps playing two words over and over and over, stuck in that loop. You pick the needle up off of the record, and move it to the next track.
My panic attacks pre-sobriety often came on without accompanying thoughts. I believe they were withdrawal symptoms. My panic attacks nowadays tend to be when I'm thinking about something stressful, so their timing makes a little more sense.
Do a little research about grounding techniques, you may find a version that works best for you.
Good luck!
Edit: Your breathing exercises are a form of grounding techniques, but there are many variations. Tactile stuff works best for me.