I'm not sure I'd call it 'shortness of breath' precisely, but on Mirena I frequently had bursts of anxiety accompanied by what I'd call 'halted breathing': like I was too scared to even make the noise of breathing. Then I'd realize I wasn't breathing properly and get even more anxious over that, causing a spiraling decent into a full anxiety attack.
I had a hard time dealing with it because in those panicked moments I couldn't remember there was an easy way out: slow deep breaths and reassuring thoughts that I was in a safe place. Maybe you could post a sign up for yourself or wear a trinket that reminds you somehow? I wish I had thought of that back when I had it in!
If you can manage to slow down your breathing to 6 cycles per minute for 3-4 minutes, your brain switches into a more relaxed state and you can pull youself out of the anxiety attack. That's 5 seconds breathing in, 5 seconds breathing out: or each time the second hand hits a number on an analog clock, switch directions.
Yes, these moments went away with removal. I've only had one anxiety attack since then (2 weeks now) and that was because I let my blood Sugar levels get too low.