Do you make out with other friends of yours? I certainly don't make out with my friends. You two aren't just friends. There are romantic feelings involved, and that means your relationship isn't platonic. It sounds like her hesitation stems either from the fact that you cheated on your last girlfriend with her, and maybe she is worried you would cheat on her; or maybe she thinks your break up was so recent, that jumping into another relationship seems scary to her. There's no way to know for sure what's going on in her mind about you and your relationship, but it's foolish to think you two have an actual platonic friendship... honestly, grow up and look at the facts here. You two clearly have feelings for each other, but for one reason or several, she doesn't want to commit to you.
I think you should talk to her about what she's thinking and feeling. Ask her why she is hesitant to become exclusive with you, and really listen to what she has to say. I would definitely suggest you two stop hanging out and participating in bonding activities reserved for romantic relationships, and definitely stop making out... and, most importantly, do not move in with her. I know you said you declined, but that would be the absolute dumbest move you could do.
Talk to her. See where it goes from there.
"Caring is not an advantage."