Do you need to worry about a cold sore around a newborn?

Yes, and this is one of the few situations where a common, mild adult infection is genuinely serious. Herpes simplex that causes an ordinary cold sore in an adult can cause severe illness in a baby under about three months, whose immune system has not developed. The rules are simple and worth being firm about: anyone with an active cold sore should not kiss the baby, should wash hands before handling them, and should avoid touching the sore and then the baby. This is a reasonable boundary to set with relatives, however awkward it feels.