My allergies cause shortness of breath when I lie down, even with medication. Your daughter needs to be evaluated for allergies, see a pulmonologist for an asthma evaluation and a gastroenterologist for a GERD evaluations. I had to go through all of these to determine my cause. Apparently GERD is a major factor.
My daughter has this problem but hers is due to her post nasal drip, which makes her feel like she is drowning when she first lies down.
Treating her room like the allergy cause can help immensely. Change her sheets weekly and wash in hot water. Get an antimicrobial/dust mite resistant mattress cover, the kind that completely covers the entire mattress and zips up. Same for her pillow and wash that weekly, too. Wash her blankets weekly as well. Have curtains, not drapes, in her room and wash them at least monthly. Dust the floors twice weekly, using a dry swiffer sweeper; brooms are not only worthless but can add to the problem as they don't collect the dust. And absolutely NO stuffed animals in her bed. If you can afford it (insurance may pay if the doctor prescribes it) get a HEPA filter for her room. These helped me immensely.