Is it possible to give myself genital herpes from masturbating with a cold sore?

So yesterday I was masturbating and I realized after I was done that I felt a cold sore coming on. It felt like a small cut that was burning slightly. Basically when you get small cracks at the corner of your lips, that’s what it felt like. I took some Valacyclovir and the next day it was scabbed over. Thought maybe it was just a small cut until I saw 2 other really small scabs and realized it was probably from a cluster. Pretty sure the cold sore came through while I was masturbating and using my spit as lube. What are the chances of spreading it to myself genitally?