Cold sore

I just noticed the onset of a cold sore near my lip last night. As soon as I noticed it I started applying medication. I have a one week old baby and I am absolutely terrified of her catching this. I’ve been crying and worrying myself sick over it because I know how dangerous and deadly it could be if she catches this. I have washed my hands, sanitized everything, made sure not to touch or kiss her, and covered up the sore with bandages. She seems to be doing normal. Has anyone ever had a cold sore with a newborn and they were fine?