Thank you for your question. Breastfeeding invariably is a stressful period, and during stressful periods, the cold sore virus can reactivate and attack again.
1) Firstly, you should get the diagnosis confirmed by a doctor and also receive treatment.
2) If the cold sore is in the mouth and you are not kissing the baby, it means that your baby is feeding on the nipple, and there is no contact. If this is the case, and you wish to continue breastfeeding, you should continue to follow strict handwashing procedures ie: before and after handling the baby.
If so, there should not be a problem. Take care.