I would be concerned too. It seems like the coughing and difficulty in breathing would be hard to ignore so it would be OK to ask her about whether she is OK--not prying. There are different medications that can help control asthma and maybe you might be reassured to know she is controlling her asthma as best as she can, or perhaps if she knows how her presentation in session is worrying clients, she might seek "the next step up" in medication for asthma control from her physician. (Maybe she is already maxed out, but maybe not.)

I think the worry that your T is overwhelmed from seeing clients could be brought up too. I bet your T knows how to take care of herself RE that issue. I think they are specifically trained for that. But still, it might help you if you told her your concern and she could reassure you about her ability to deal with her daily pressures.