The best thing I have found for coldsores is Carmex ointment. It is like a medicated lipbalm you can get from the pharmacy and it's main ingredient is camphor and menthol so no harm to the baby. I have suffered with cold sores my whole life and couldn't live without my Carmex lol. It is my general lipbalm also which prevents the onset of the sores smile
Hope that helps!
(I'm not sure if you can take them while breastfeeding but I also take Lysine tablets to eliminate the sores, maybe ask the chemist?)