The only thing that I can think of is if you are biting on a large cube then you could crack a tooth. Brain freeze is possible but that passes. I have choked on an icecube when i was young. It got caught in my windpipe. I coughed it up but it scared me. If you are eating small pieces of ice it won't hurt you that I know of. When you eat ice cream or a slushie you are eating ice.
Eating ice doesn't cause anemia. The craving for ice is usually an indication of iron def. anemia.
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