Cold Sores = Herpes?!?!

Hey guys so I’m kind of freaking out right now. My significant other has a cold sore which means that he has the herpes simplex virus HSV-1. This is NOT the one associated with genital herpes. I am concerned though because online it says receiving oral sex from someone who has HSV-1 can actually give you genital herpes. What are the chances of this happening? Have any of you gone through this?!