Would my g/f gets sores down there if I have a cold sore in my mouth and I performed oral?

Herpes. Yes and no. This answer is complicated. But, if she has herpes type one from a previous exposure she cannot get it again and it cannot be given in a different part of the body. At least 75% of americans are thought to have herpes type one. So, if she has not been exposed previously (she and you both need the blood test for herpes) then she can get herpes type one on her genitals.