Cold Sore with a Baby

So Wednesday I didn’t know what this thing was because it was just a little more red than my actual lip so I didn’t think anything of it. I kissed my 3 1/2 month old. I mean it wasn’t bothering me at all or anything, I thought I just bit my lip to hard or something (bad habit of mine). The next day it actually turned into a cold sore....... is my baby okay ☹️☹️☹️☹️ I called the nurse line and they were saying they think she will be. But has anyone had similar experiences?