I think the reason why you think it's not going to work, is purely because you don't think very highly of yourself. Sorry if this is completely incorrect. but it seems your self-esteem is so low perhaps you might feel that you aren't good enough for her?
Which is complete BS from what i've read. You actually care about this girl. So I love what your friend said and in his words exactly:
She is yours.
Stop feeling like she's gonna cheat on you, and enjoy your relationship with her. Each relationship you learn something. Every single relationship you are in teaches you more about yourself and you can grow and develop in yourself. Even if it "fails" it's NOT a failure. It's a learning curve. I have come from a relationship that was destructive, and it has made me who I am today. I am stronger because of everything I've been through.
Anywho, just enjoy your relationship with your girl, if it last awesome if it doesn't than LEARN from it.
Stop feeling that you're not good enough and enjoy your life.
Carpe Diem! or "seize the day"
Just enjoy your life, enjoy your relationships because they teach you so damn much!