I think my girlfriend wants to say she loves me?

You can't love someone untill you know what kind of personality they have, and you say you don't 'think' she is affectionate, which means you're not realy sure about her character. Affection isn't all to do with physical contact, it's about the way we communicate verbaly with one another too. Does she tease you and play with you, or is she a little shy and restrained? It sounds to me like you both need to get to know each other a little better and just have fun with each other. Maybe the love will come later.