Your daughter very likely has an absorption issue in her gastrointestinal system, thus preventing her ability to absorb iron (and likely other nutrients). 2 initial areas to investigate:

1) Run a lactulose/mannitol test to rule out Intestinal Permeability (Leaky Gut). This condition is quite common and often leads to the symptoms your daughter is experiencing, including the acne on her back. Leaky gut is often fixed by identifying offending foods (test for possible hidden food allergies/sensitivities), and correcting the microflora (good bacteria) in the intestinal tract. There are 10x more microbes in our body than all of cells put together - thus a slight imbalance can have a large impact on how we look, think, and feel.
2) Rule out Celiac Disease. This is a condition that is a severe reaction to gluten containing foods. Gluten is found in barley, rye, wheat, spelt. Celiac can create severe malabsorption of nutrients, including iron. A simple blood test will help to uncover if this is an issue for your daughter.

I hope this is of some help to you.

Regards,
Dr. John Dempster, ND
www.thedempsterclinic.com
416-551-9577