wills, i bet most of your 'falling apart at the seams' is due to sleep deprivation. once you get a good rest, your own experience will be enormously valuable. how old is your dd?
my dd, 3, has asthma. it vanishes for the summer but kicks in at wintertime. we're lucky -- the only symptom (touch wood, ha ha) is a night cough. the aftermath of colds is always bloody, i know. before your DD had the measles, did she night-cough?
the thing to remember (someone pointed this out to me on MN a week or so ago, my GP had failed to make it clear) that if the cough persists at nighttime then the medication needs to be revised. after 7 wks of disturbed nights, this information gave me courage to go back to the GP, at which point he gave her a short (3-day) dose of prednisolone which did seem, by the end of the course, to have had an effect. we had a good week of quiet nights, but now she has got another cold so we're in for fun again. this time i certainly won't let it go for 7 wks.
i'm assuming your DD is on the inhalers? dd was given them when she was a little older than a year. have you got an action plan from your GP, ie advice on how to up the dosage at the onset of a cold? perhaps you need a referral to an asthma specialist, or a paediatrician?
we try the bed-tipping too when she has a cold. a warm-mist vapouriser (you can get them from argos, they're a fiddle) may make a difference. i do calpol, the vicks on the chest thing too, all the usual coldy things, while the cold is still present.
the National Asthma Helpline is good -- there's a website too with a section on children, but the people on the phone have been very useful/reassuring.
feel a bit like i'm teaching my grandmother to suck eggs here, YOU'RE the expert, but i do HTH.