Weird situation with a girl, don't know what to do

I've known this girl for 3 years, throughout uni. And we always vibed, and were always close with each other (like cuddled etc). But we were always friends, until her friends said to her that they think I liked her, just from how I looked at her in the club one time. From then, she started to distance herself from me, as she got overwhelmed. At one point, she confronted to me about it, whether we should become more that friends. And I'm now at the point, where we have been on a date, but she is not giving any energy back. So basically I have to be the one to initiate it everything, but she doesn't at all. And I told her that, and she said she feels like I'm just dating her because her friends mentioned we should be together. But I actually do genuinely like her. So I'm at weird situation, where we are like kinda more than friends, but at the same time it doesn't feel like a proper relationship cus she feels like I don't truly like like her. So what should I do at this point to make her trust me?

This happened to a relative at mine at uni. She and he were best friends, flat mates and his friends putting on pressure, 'you should be together' all the time. Eventually he developed feelings for her and he never told her for 2 years. By the time he did come clean, he was in too deep and she said I only see you as a best friend.
He took off and not spoke to her for a whole year. He blanked her when the group got together. He eventually apologised for his behaviour recently. So dont let things carry on and feelings get involved on one side (and for ages). Unless you are getting feelings from both of you, then its just best to stay as friends.