Thanks for your question.
The short answer is: No.
Cold sores are not inherited, but passed through direct skin-to-skin contact.
Having a cold sore does not mean you have genital herpes. Genital herpes can be passed to children if the mother has a genital outbreak during childbirth.
Cold sores can be passed to your child if someone with an active cold sore kisses (or has mouth-to-skin) contact with your child.
Herpes in childhood is very common, and not a serious condition.
For more information about HSV and cold sores check out our Herpes – Patient Guide.