Cold sore on Momma

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The cold sore virus runs rampant in my family and my husband’s. Of course I just got the nastiest one. I want to take L-lysine so bad because that helped me pre-baby but I also BF and I don’t think there’s much research.. anyone know more about this? And from anyone’s experience, when did you go back to kissing baby? I never kiss near her mouth in general but of course everywhere else lol I was going to wait until it appears completely gone but sometimes my skin stays a bit tender & pinker for awhile. Any advice?