I think there's a bit of confusion here. It's the herpes virus which causes cold sores, not hepatitis. Usually people get the cold sore virus as a child & I think around 92% of people have it. Usually it raises it's ugly little sores when you least want them - often when you have another illness or have been out in extreme hot/cold weather. I have had both eczema & cold sores throughout my life but as far as I know one doesn't affect the other. The only possible problem I can think of is transferring fluid from a weeping cold sore to broken skin on eczema.