How to make girl friendships? (F19)

I (F19) have seemed to struggle my whole life making friendships with girls, despite always trying. Im about to start university (college for Americans) and all I would like is to make some friendships with girls, I am so worried about it because it has never really happened before. I have only ever had strong friendships with guys, only due to the fact that they never seem to think im weird, and always want to be my friend first/accept my friendliness. This is really sad to me because Im worried that girls will just never like me. I have one close best friend (F18) who I met at college, and I can assure you I am a kind, respectful friend to her and to anyone. However, whenever I have approached any girls to make friends previously in life, they often judge me, or think im weird. I have been laughed at for trying to make friends with girls before.

Im happy to provide more detail, I am so desperate to find out what is wrong with me, or for even any small help on how to approach girls to make friends. I dont want to be alone at university- or worse- called a “pick me” Thank you :)