I want to look through my gf's downloaded messages on facebook
What are you hoping to find in the messages?
I'm want to find out if she really loves me
I think that you should just ask her. Going through private conversations is not okay. You might even find something that you do not want to see.
It's Facebook messages for Christ sake. I will only look through it if I find her in there cheating with someone.
Are you concerned that your girlfriend is cheating on you? It's better to confront her directly and share your feelings rather than going through her private messages. You won't know what you find until you're already looking through them, and by then you will have already invaded her privacy.