Are cold sores related to anything std related

I would get cold sores a lot and I saw it’s a type of herpes. I was wondering if that has anything to do with any kind of genital herpes. My first sexual partner gave me oral and the next day he had a cold sore. I’m worried if it had anything to do with that. Once it went away we went back at it and nothing happened after that. I really don’t want to go get checked out either :/