Guys, I told my gf to not touch me in public, she became distant. I need advices?

I'm a 24M, and my girlfriend (23F) and I have been together for 8 months. It feels like longer because we've been through a lot. What initially attracted me to her was her looks, but she wasn't the best at communicating. Still, her laughter drew me in.
From the start, she acted like we’d known each other for years. She always plans our dates, and I usually just pay. But here’s the thing—my girlfriend grabs a lot of attention wherever we go. She’s very pretty, and the way she walks, laughs, and dresses makes everyone stare at her. I know she’s not trying to get attention, but her whole vibe draws eyes.
On top of that, she's much more sexually forward than I am. For example, when we’re at a party or even at a movie, she’ll pull me aside and ask me to touch her or kiss her. She’s not shy about it at all. She’s always initiating things, and I get worried people will notice, or that it’s too much for public spaces.
One time, at my family’s house, she went to the car to “grab something” and called me out there just to ask me to touch her. She put my hand in her p***sy and rubbed it with it, she was wet wet. It's honestly overwhelming, and I started feeling uncomfortable, especially in public. i feel embarrassed and ashamed. its as if everyone will see us, maybe they will notice her. i know her horny eyes, what if others see her?
In class, she’ll link arms with me or touch my hands constantly.
I finally asked her to stop touching me in public, which upset her. She said she acts this way because she’s happy and likes me. Now, she’s stopped all of her usual behavior, and for the past 8 days, she’s been distant, treating me like everyone else.
What do i do? did you ever experience anything like this? i am sorry if you arent used to questions like this but i need public opinion.

I’d maybe sit down and distinguish what type of touching bothers you exactly. Tell her that you don’t mind handholding or a quick peck, but that sexual touching in public crosses a line.
Reassure her that you care about her, and are attracted to her, because she might have understood you asking her not to touch you in public as a rejection or lack of attraction to her.
Be very clear in your communication of boundaries, and what is and isn’t ok for you. If she still continues to cross them after that, then she’s not respecting your boundaries and you might need to rethink if a relationship where your boundaries don’t matter is right for you.