The fly mask does help shade the face. If there is any way you can, I would suggest keeping her inside during the day, or some place that is completely shaded. Another thing you can try is spraying sunscreen on her and brushing it in. It protects the hair, and if you brush in thoroughly, it also protects the skin. The kind I use is Quic Screen. It lasts a few days as long as the horse is not washed/rinsed/exposed to a long rain.
Fly sheets help protect from sun damage. Here is just one example Amigo Mio Fly Sheet - Dover Saddlery.
If you want to be sure that a fly sheet gives enough sun protection, look for one that lists UV protection as one of the product features.
Hope this helps