We had an amazingly fluid and natural time together, could've done more sexual talk, but because she was driving us around, I hesitated to kiss her. I wanted to go to all the places we were going, and didn't want to risk it. On the way back to her place, I put my hand on her leg, and she says that she's not looking for a relationship or anything physical. I tell her I'm not looking for a relationship either, then change the subject, but leave my hand on her leg for another 3 minutes.

We get back to her place, and we are out in the cold, and she asks for a hug goodnight. I give her one. She compliments my smell, I do the same to her, then go for the kiss. She's not engaging much in it. She say's she likes my kiss, but that it's a little much. I'm freezing and starting to shiver, I suggest we go inside, but she declines. Probably should've pushed it. I kiss her goodbye. She seems a little taken back, and surprised.

What do you think I should do, or could've done differently?

Seems like you hit it off pretty well, she's probably the "taking it slow" type. I wouldn't take her comment about not wanting a relationship seriously, this type of girls is just cautious about being played. They view sex as something special that shouldn't be done the first night... I guess she had no intention to invite you in, so not pushing was the right tactic. The only problem I see here is that she was driving, e.g. in control of the logistics. This also implies she was not drinking, which would have loosened her morals a little bit... My guess, it will take you some 2, 3 dates before you seal the deal... Good luck!

She texted me back, after I invited her to go shopping for clothes

Her: I'd like to hang with you, but I feel like we're on two different levels with where we're comfortable physically.
Me: Word, well I think we are both flexible people and we can adjust to get on the same comfort level. So what's up, you want to come?
Her: No, I think I'll pass, thank you for the invite though
Me: Alright, well when you see my new threads and you're jealous, don't blame me
Her: Lol, I understand

So I'm not sure if I should try to chill with her again and escalate further, or fake friendzone her and tell her that actually I think we should just be friends, then escalate, hah!

What you think?