Yes, as lwhuntley4 says, your parents were 13 going on 14 themselves, once.
And, as a parent of a 13 year old and of two older boys I can tell you that parenting is not easy. I'm not talking about parents with problem teenagers ~ just general parenting. Parents are just grown-up children, you know.
I tease my kids sometimes ~ sometimes it's to try to help me communicate better ~ sometimes it's just who I am, and they tell me off for showing them up.
And what if they do tease ~ it's not the end of the world; it can be a sign of affection.
I suggest that one possible idea might be to go our with this girl, but just as 'friends' for now. Let your paents take you both ~ or go with a couple of other friends and let parents decide who will take / collect / accompany ~ let your parents get to know her, then let the friendship develop naturally. Just keep your parents informed, so that they are not worrying about you.
I'm glad to hear that you are being thoughtful, sensible and responsible, by the way ~ but do your parents know about your decision:
'I took a "class" about sexual activity and I'm well aware of why it's bad to do it at this age. I promise myself to not have sexual activity for many more years.'
They might take you more seriously if they knrew that there was more going on in your head than videogames.
They won't find that out if you won't communicate with them though.
Good luck!
