@RB Coop
I always feel this is the hardest part to deal with, how to manage injuries. You want to be responsible and so on, at the same time not risking that the trainer won't invest in you. Add some language barriers and it gets complicated
I try to downplay any kind of injury but that's from a woman point of view. Some trainers are very traditional and think girls are much more sensitive so if I start talking about some issue it becomes a big deal.
Anyhow in muay thai everybody is injured. If I were you I'd not mention it at first, try out the training, test your limits and how you can manage. Most likely your trainer will notice if you're in pain and if you need your asthma medication and will be able to determine whether you can fight or not regardless of you explaining your health issues or not. And probably you're not the first fighter with these issues he's trained.
I've seen it many times where a newcomer arrives and directly goes to a trainer and explains everything about themselves and what they want and need and cannot do and the trainer is always like "yeah yeah" but my interpretation is what he's thinking is "let's first see you train".
Just my two cents.