cold sores?

do any of you mamas get cold sores? what do you do to protect the baby from it besides no kissing and washing your hands? i’ve never had a cold sore before but the past two days right under my bottom lip has felt super itchy, and is red. im scared this is a sign i might be getting one. i want to do everything i can to protect my baby from it because i know it can be fatal to babies. he is 11 weeks old. please let me know. thank you!