Cold sore means herps?

Okay so my mom just freaked me out. For the very first time yesterday I got a cold sore for the first time of my life. So I told her because I was so amazed on how fast it went away. So she told me I need to get checked out because it can lead to herpes. I went into shock! So I'm like I don't give oral sex and I don't kiss after anyone gives me oral sex....
Does cold sores lead to HSV(herpes)?!