I (27F) have a new friend (33F) that keeps overstepping my boundaries, how do I move forward?

Sorry for the long post there’s just so much to share. And this isn’t even everything. I (27F) have a new friend (33F) that keeps overstepping my boundaries and I think she is obsessed with me in a concerning way. A relevant detail is we are both lesbians.

I’ll call her Sara (fake name). When we first met she approached me at an event and I told her I was not looking to date and was only trying to make friends. After hanging out once I got the vibe that she wouldn’t be able to just be friends with me. I sent her a text saying that I didn’t feel comfortable pursuing a friendship if she was going to hold out hope I would change my mind about dating her and that I didn’t want to lead her on. She said she didn’t mean to overstep my boundaries etc. I left it at that and we went months with no contact. We ran into each other at the same concert and us and our friends hung out, it was fine and I was okay to just be friends.

After said concert I went through a rough few days and she was there to comfort me which I appreciated because my friends and family are states away. She would check in everyday and it was fine. I’m no longer going through said situation but she seemed to be convinced I was still upset. She is a therapist so she was psychoanalyzing me constantly, observing I have control issues, anxiety, hyper independence etc. which I’m all aware of, but did not ask her opinion on.

A couple weeks ago she asked me what my love language is I said quality time and physical touch. She then proceeds to awkwardly touch my arm. I said “but not with my friends. I like physical touch from my partner when I’m in a relationship but with my friends it makes me uncomfortable.” She then goes to the entirely opposite end of the couch and acts all weird. Instead of respecting that she would say “I’m going to lay my head on your should okay?” Saying it in a weird soft tone and do it anyway. It’s very uncomfortable. The other day she kept touching my face. The first time caught me off guard so I didn’t say anything but the second time I gently grabbed her hand and redirected it to her lap and tapped her hand as if to keep it there. She asked if I was overstimulated, I said “yes” because I always am around her. She said her being extroverted (I’m introverted) and physical touch is all really good exposure therapy for me. I said “we don’t need to do exposure therapy for physical touch because that’s not going to change.” I have quite literally a million other examples of similar things, where she’ll do it and I’ll say I don’t like it or redirect. My body literally recoils/cringes when she touches me like it’s so uncomfortable. It’s not like that when I give other people a quick hug or if a close friend leans on me. However my friends know I don’t like that so it’s rare.

She also gets weird when I mention other friends. I was out with Sara and her friends and I had another friend (ill call her Taylor not real) who is not involved with Sara’s friend group ask if I was busy and wanted to go out. I said I was out with Sara and she could meet up if she wanted and told her where we were. I told Sara that Taylor might meet up. She got kind of weird.

During a conversation weeks ago she had asked me if I was going to go on dating apps or hook up with people and I said that’s not a priority right now. I had mentioned that I went on a date with some one MONTHS before I ever met Sara. I said that I had had a good time and liked her but I wasn’t ready to be involved with anyone so we didn’t go out again. Flash forward to a few days ago, Sara was in my car and a text from said girl I went on a date with popped up. I had been texting her a little but not too much, she’s friends with Taylor and she mentioned that she was possibly interested still. Once she saw the name she got weird and was like what? And I said “oh she texted me after I hung out with Taylor a few days ago.” Silence. About 20 minutes later she asked if she had asked me on a date. I said no it’s just small talk. Later Sara asked if the girl were to ask me on a date if I would go. I said “I’m not sure. I would want to because I did like her, but I don’t know if it’s a good time for me.” Awkward after that.

She also does grand gestures for me. She gave me a laptop because I mentioned I might want to take classes in the future. She told me she was going to get a real piano to put in her house and give me a key so I could play it whenever, I had mentioned I loved to play but my keyboard didn’t feel the same. And there’s a concert coming up I said I wasn’t going to go to because I couldn’t pay for the expensive ticket at the time and she bought a ticket for me. She insists on paying for me constantly. I’ve expressed after each thing that it’s too much and I’m not comfortable with it. She said to just lean on her. And I said I’m not comfortable with leaning on her especially financially. She knows I’m working 2 jobs and struggling. I do not want help from her, I am self sufficient.

The other day she asked if I would ever tell her if I was gonna ghost her. I said I wouldnt ever just ghost her. I said like I sent a text months ago saying I wasn’t comfortable I wouldn’t just ghost her without expressing why I would be taking a step back. It’s almost as if she knows I’m uncomfortable but it doesn’t register?

At first it was just annoying but now I’m genuinely concerned because I am constantly uncomfortable around her. She is so overbearing that I can’t just step back entirely without saying something. However I feel I’ve been direct and I’m at my wits end. It’s only been like a month of being friends and I’m going insane. Help!