Asthma and Atopic Dermatitis usually exist together and the best part is that both are likely to get better and better as the child grows in age.
Nebulisation is pretty safe though not if given almost on daily basis. There are prescribed regimen for treament and prevention and I suggest you stick to them under able guidance of your Doctor only.
For prevention, get an annual dose of Flu vaccination for your child every year. Second, avoid those food products like cold water, ice-creams and toffees which may be triggering such attacks in your child. Good luck.

Hello
Thanks for the query
There are so many pointers suggesting your baby is suffering from asthma. According to treatment guidelines it seems she is in the stage of mild persistent asthma. According to Global initiative for asthma low dose steroid( budecort) is in treatment guideline of asthma as 'controller' medication and levolin as 'reliever' medication. The side effect with the use of steroid is effect on growth, which is also your main concern. An approximately 20% reduction in growth velocity is noted in first year of use. Subsequently the growth recovers and children ultimately attain the predicted adult height. The another problem is oral fungal infection following use of steroid. To avoid this rinse the mouth with water everytime after inhalation of steroid.
Keep the child away from allergens( dust, animal fur, smoke, tobacco etc) avoid sudden change in environmental temp., avoid cold eateries, make a chart of weight and height of baby. You can download GINA pocket pediatric for asthma control from internet. You can get the performa for regular home monitoring and also other imp. information for management of asthma.
I hope this answers your query well
Wish you and your family good health
With regards