Yes eating ice is a symptom of iron deficiency, and iron deficiency can cause hair loss ( there are other reasons for hair loss). I suggest you get a blood test.
Is Eating Too Much Ice A Symptom Of Iron Deficiency And Hair Loss?
Can your nerves cause you to constantly itch and break out in sores
I have anemia and yes I eat lots of ice, I actually crave it. My dentist isn't so happy and neither am I but I just can't kick it.