Has she had her adrenal gland function tested? Thyroid med. will affect the adrenals, and vice versa. It can be difficult to balance hormone levels between thyroid and adrenal glands after starting synthroid. My son started having panic attacks too. He needed to go on hydrocortisone for adrenal insufficiency. I think your daughter should have another cortisol level test, either 8 am cortisol, or 24 hour urine test... Both would be best. (I'm assuming she had one done before her doctor put her on Synthroid).
If thyroid hormone is too high too long, you will eventually cause adrenal fatigue. Many people whose numbers are in the normal range on tests still don't feel well. It can take a long time for a body to adjust to synthetic hormone replacement.