Your involuntary nervous system knows how to breath enough without any intervention from you.
It sounds like you have emotions coming up that are making you anxious, and perhaps stimulating your system to breath more.
I’m assuming you are getting proper medical care for your asthma.
About 5 years ago I got pounded by anxiety for the first time in my life. It made sitting very difficult.
I experimented with a lot of variations on the way I meditated and I experimented with different techniques to get me calm. None were magic bullets but all helped.
At the worst of it I found talk therapy, talking to people who cared about me, exercise, very very long walking meditations to be the most helpful.
I tried a number of other things and I am willing to throw those suggestions at you if you are interested and ready to take the emotions you are dealing with while sitting.
Good Luck either way.