OP -- I don't have an issue with cigarette smoke (father's an inveterate smoker and so, I barely even register the smell).

But, I am extremely sensitive to most other strong smells (and asthmatic too) -- E.g. heavy duty perfume, lotion and the like.

There's a client before me on specific days who, I dunno, bathes herself in some gawdawful perfume or something and it's like an assault on my senses. I just tell my therapist about it and she's like "Yeah, that person wears that flowery scent" and I make my displeasure clear and we move on.

But, if I was actually having a hard time breathing -- like you do -- I'd request to move elsewhere (outside / a different room) or basically, just say that this isn't working for you. What do you have to lose, really?