Can someone be addicted to drinking their own blood?

There's nothing in blood that will make a person addicted to drinking their own blood. If a person does get addicted for some reason, it's most likely a psychologically problem. Absolutely no, as a clinical addiction requires a physiological component. A psychological "addiction" more correctly a habituation, may however occur. Drinking your own blood is dangerous in that there is an infection risk. Also, there's the risk of masking other symptoms like a a gastrointestinal bleed. If you feel compelled to drink your own blood, I kindly suggest that some counselling may be helpful.