Me and my girlfriend have a physical mismatch

My girlfriend and I have been dating for four months, and are juniors in high school. This is both of our first relationships. She has never been romantically involved with anyone else while I had a situationship about 6 months ago.

Lately, a new issue in our relationship has been physical affection, private and public. She is a germaphobe and isn’t comfortable with any physical intimacy in public.

I’ve asked to hold her hand while walking between classes, and she’s always said no, which I’ve respected. We have talked about it privately and she’s very uncomfortable with it, but willing to compromise.

About a month into dating, I asked to kiss her, which I was rejected. I’ve expressed how I wanted to kiss her, but it’s likely not happening for a long time. Her germaphobia is the big thing, she’s also very uncomfortable with spreading germs between our mouths, which yeah sounds kinda gross but still.

We’ve talked about compromising, with her saying she’d try holding my hand in public, but I’ve never acted on it.
I don’t really want to do anything she doesn’t want to do, and if holding her hand makes her uncomfortable then I won’t, but at the same time I feel disappointed that she isn’t doing these things with me.

When I think about suggesting getting more intimate privately, it makes me feel like a creep and I back off. I can also already anticipate her answer, which is no.

I don’t know what to do, I’ve just been kinda sticking it out and seeing what changes. We both really like each other, but this is a big hurdle for me.
Advice is appreciated but this is mainly just to get this off my chest as I have no one to talk to about this.