And you're not joining letters, you're making friends. We could spend hours on why you think you are not "best girl" but most of us are not literally beauty queens, but still have something great to offer. I for one have a charming way with humor and sarcasm (

) and a fantastic ability to organize. But was I Gamma Phi material (on my campus)? No. Am I sorry about that? NO. I would not have wanted to be on 24/7 and I have to think there was a certain pressure there to look great all the time.
I think as rush can be such a blow to your self-esteem, it would be very healthy for you to spend some time thinking about what makes you awesome. If you are REALLY short on self-esteem, maybe you can talk to a very trusted friend or your mother. Rush is no time to be self-depricating, but knowing which of your MANY attributes to cheer about might take some forethought. Put yourself together a play list of girl power music (I Am Woman by Helen Reddy comes to mind but there are plenty that are much more current), and write out, even if for your eyes only, what makes you great. Then burn it if you have to but try to keep the message in your heart. You undoubtedly have something a sorority wants - you just have to find the right marketing and packaging so they KNOW you are who they want.
If your concern is your physical appearance, what can you do about that in the couple weeks before recruitment starts? Maybe get a rockin new haircut, a full make over (and learning how to apply the makeup), a wardrobe overhaul overseen by someone you think has awesome taste. If you think you are not rockin it now, then obviously there's something you would like to change. So change it! That can feel like a leap into the deep end, but it might be the self-esteem boost you need right now.
Good luck!