Average GPA At An Ivy League School

I graduated in 4 years from an Ivy League school with two majors. However, my GPA was average and not high enough for medical school. In the year after college, I've wanted so badly to get back on track that I've studied 2000 plus pages of Kaplan MCAT material and a USMLE book, and have done every problem in my organic chem textbook and my physics book. I also have spent time volunteering with a professor at UPenn and at a cancer hospital to ensure I get good recommendations for med school. Additionally, I've been reading science daily articles about the results of new studies every day so that I have a solid knowledge of current medial developments. I know that one day I will truly deserve entrance into med school if I never give up, but my motivation is waning and I feel so discouraged now. I hate myself for not being good enough at UPenn and it's so hard to get myself to keep studying for a career path that I don't know if I can ever have. But even a year after college ended, I keep on studying!