Listen, I know no one wants herpes of any type, but it's never a good enough reason to end a relationship.
About half the adult population has it, and 90% of those never get any symptoms. You could have it and not know it. If you break up with her, the next woman, AND the next woman you date could have it.
That said, if you are someone who has a big fear of germs, then this relationship isn't for you, and to be fair to both of you, maybe you should end the relationship. You should allow her the chance to find someone who can handle a cold sore.
If you live in a place - the UK or Canada, for example - that doesn't offer blood tests easily, you may not know if the next partner you have has it. You may be safer with someone who has it and knows it and can take daily suppression and knows when to avoid contact.
Your girlfriend should definitely not perform oral sex while she has a sore present, and shouldn't until it's completely healed. We know it can transmit during shedding, but we don't know how much virus it takes to transmit, and that may be different for each person. There may be days she is shedding that you don't get it, if you don't already have it, and another day that you might get it.
So ultimately, it's up to you. If you truly don't think you can handle the possibility of getting it orally or genitally, then this isn't the relationship for you. If you do end it, then do so gracefully. Let her have some dignity, and don't tell everyone this is why you did it.