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So I’m a little confused. You have HSV 2 but somehow you think your HSV 2 is oral, not genital?
It does appear that you daughter does have HSV 1 infection, which is not that unusual for a person her age. Do you also get cold sores (normally HSV 1)? She would not catch your genital HSV 2 infection through sharing a drink but maybe I am not understanding this correctly? Can you clarify?
By the way, the antibody test (and I”m assuming you that you mean that you had HER antibody tested) is not great for children of her age. There is a 50% false positive rate in children on this test. It was her, not you, that was tested?