My daughter has suffered HORRIBLY from excema since she was a baby and is now 10 (no asthma).
This is the deal - NONE of the prescription creams are safe long term. The problem is the over-the-counter creams that are safe, don't heal a flare-up. They are good at reducing and preventing more flare-ups or the intensity of them, but they don't really do anything to heal a flare-up. Also, once the skin is broken ,red, crusty and rashy, those creams REALLY STING when applied.
The trick is to use the prescription cream prescribed by your docter (mine alway prescribed Elidel) for the shortest period of time possible to heal the flare up (no longer than 7 days- but less if possible) once you are done using the prescription to sooth the flare -up, then don't miss a day of slathering all effected areas (even the dry bumpy areas) with Eucerin Calming cream or even just plain Eucerin (we have found these to be best, way better than Aveeno). That will keep it from rashing up again.
Bathe her once every other day , short bath, just get the hair washed and quick wash the important areas using a non-scented glycerin soap. Luke warm water, NO hot water. Slather with Eucerin IMMEDIATELY after drying off from the bath.
My daughter suffered very badly as a toddler, but is getting better as she gets older, although I mostly attibute this to the fact she is old enough to apply her cream every night before bed her self and it gets done more regularly. She uses the cream as soon as she starts to feel dry or itchy, rather than letting it go until it bleeds and I would notice it when she was a baby.
The trick is to keep it at bay with over the counter stuff, and only use the prescriptions stuff for a short period of time to heal a full break-out. They won' hurt her if used the way the doctor prescribes (under 7 days)