M.F.
There are nothing but horror stories online, so do yourself a favor and stay away from Google.
I am like you, cold sores occasionally since childhood and got one when my son was only a few weeks old. I was concerned because I know the Herpes virus in infants becomes systemic, I was nursing and I am a big kisser. I used alcohol on a cotton ball to dry it up followed with Abreva every chance I got, took oil of oregano and put that on the cold sore also (natural anti-viral), I washed my hands religiously, changed my pillowcase often, stopped nursing him while sitting in my bed, made sure he didn't touch my face and no kisses anywhere until it was totally healed, not a tiny bit of scab left even. I kept a close eye on him for signs of any illness-cold symptoms, high fever, not just sores on his mouth-prepared to run him to the doctor immediately if he displayed any symptoms.
He was fine and I started taking Lysine supplements to prevent another breakout, at the suggestion of his pediatrician, who also battled cold sores. You're more prone to get them when stressed, hormonal and sleep deprived, as all mothers are.
Be very cautious, keep vigilant and if he does show signs of illness, take him to the doctor and tell them he might have been exposed to Herpes. Other than that, call his pediatrician if it will help you stay calm and try to just ride this out.
Good luck!!