I want to prove to her that I'm better than the rest...?

I like her a lot and unlike some other guys when I like a girl I like her, I'm not just trying to get into her pants. I know she had a hard time, her dad commited suicide on her birthday when she was 7, she went through abusive, worthless relationships. We hang out here and there as friends but I want it to be more. Does this mean anything? She gave me her bracelet, took my necklace and put it on and kept it, we held hands, hugged, and sometimes when I drive with her in my car I see her look and when I turn to look at her she looks away and smiles, calls/ texts me not always but always initiates. Problem is she just got out of a relationship and I can see her going through hard time (she cries, drinks sometimes and calls me crying :(. I am not in a hurry and can give her time to heal and move on but I am so scared that she will find some other guy, or go back to her ex who she still has feeling for prob... she said noooooo relationships for a while and she's over her ex but idk. On her birthday I want to be the first to say "Happy Birthday" get her flowers, a glass rose and a card with a sweet letter/poem inside. Should I?