I have mild misophonia, so I do sympathise.
I never thought of my hatred of the television being just background noise as misophonia, Navy, but I guess you are right.
Apart from that, I especially hate slurpy eating, and squelchy chewing. I am actually very sensitive to my own eating noises, as I am worried they will be upsetting others.
But I do think you need to take a step back and focus on your DD, Lumpy. I'm sure she's not doing it to push your buttons. She just feels like shit, and wants her mum.
Instead of asking her to breathe normally, why don't you acknowledge that it is you with the problem, and that she is doing nothing wrong. Do everything practically that you can to help her, but just explain that sometimes her breathing noises (which you know she can't help) get too much for you, and you need to go out for a while, and ask her to respect that, and just give you some time to pull yourself together.
Also, Vicks does start work to clear the sinuses instantly. It doesn't take 20 minutes. Your breathing keeps improving for a while, but it does start getting better right away.