Nizral has Ketoconazole
as its active ingredient- which is the antifungal used routinely.
Usually minor fungal infections and dandruff
affecting the eyebrows- respond well to this.
Since its almost 5 months and no improvement is seen, its better that you see a Dermatologist
before further conclusions.
Like antibiotics, improper use of anti-fungals too will result in resistance. They might not work when needed.
Regarding probiotics- there is no harm in using it for a short period of time. Certain infections and allergies of skin do respond to probiotics. But its always advisable to use them after doctor`s advice. Instead you may use lot of yoghurt which contain probiotics naturally.
Please do visit your Dermatologist, get the diagnosis confirmed and get your daughter treated properly.
Hope my answer helps you.
Wish your daughter good health.