I don't believe in twin flames at all, but what you are describing is extremely familiar to me and I've felt it before. It reminds me A LOT A of this thread I made several years ago:
https://www.infjs.com/threads/why-is-this-happening-to-me.36540/
Essentially, I was obsessed with this open mic host and was for at least a year. In the exact same way that you describe with this girl. I got his phone number and would text him but he never really texted back a lot, he would talk to me at the mic some nights and was really friendly and then other times wasn't. I felt very connected him, and I was convinced he also felt connected to me even though his behavior towards me was hot and cold.
In order to explain the behavior I was also convinced he was sending secret messages to me through his behavior. It was a whole bunch of mental gymnastics that I did because I REALLY wanted him to like me as much as I liked him, and I never confronted him about it because I didn't want him to reject me, so I thought, oh well, eventually it will just happen. I can convince him somehow of what I know he feels about me deep down.
The last 3 years after that were really hard but great years because it happened to me over and over again with different people. I realized I was experiencing limerence because I never dealt with my childhood trauma and thought love was going to solve all of my problems. I felt love was the only thing that would complete me as a person because I had never been loved before, not even by the people who were supposed to love me, my parents. I did not think I was lovable or worthy of love and I genuinely believed that because of that, I needed to cling to people who were nice to me and convince them to fall in love with me because I needed that.
I finally learned to stop objectifying men that I found sexually attractive and look for people who are actually compatible with me on a life level. They were not my fantasy- they did not bring me larger than life highs or the feeling that if I didn't have them I would die. It was less exciting. But it was real. I am in my first long term relationship and I'm learning how to love somebody finally. All because I stopped pursuing people who didn't want to be with me and was realistic about what would actually be compatible with me instead of this ideal image of the type of person who if they loved me would make me lovable. Stopped trying to win people over.
I can't speak on your experiences, and I'm sure what I experienced wasn't what would be considered a real twin flame according to the theory. But I relate to what you are saying... Whether or not I really experienced what you're talking about or not.
I decided to stop living in fantasy and live in reality... Because that was what was real. I didn't need to tell myself stories or live in hope anymore. I could handle the truth, no matter how lonely or painful. I learned to survive. And I still found happiness. In fact... That's the only reason I did.