I will try to tackle this one since nobody else has bothered to reply:
1.) You are not in competition with your friend at MIT. Perhaps you two will apply the same year, and be in the same applicant pool together. It is highly doubtful that you and her will ever be compared side-by-side. There will be around 8000 applications in the mix with you guys at each school.
2.) Public universities--there is nothing hurtful about attending a public school. Some of the best schools in this nation are public (ex- UNC, UVa, UM, U Il, UCBerk, UCLA, etc). However, what you do at this public school is what's going to matter. If you pull at 3.4 at a pub school, it's not going to measure up to a 3.4 at MIT or any other big-gun private school. However, if you pulled a 3.8+, you are just as competitive as a student from MIT. Yes, you will probably lack some of the connections/benefits she has by having a MIT degree next to her name, but it's not going to prevent you from going to a good med school.
3.) Quality of education- She's going to have smaller class sizes and more interactions with her professors, but that's why she is paying PRIVATE school tuition. Public schools cannot afford to keep class sizes small, they don't have the funds for it. Is she going to get a "better" education than you? That depends on if she utilizes the vast resources before her, and if you utilize what your pub university has to offer you too. I'm not sure what school you go to, but I'm going to guess it's UMaryland, which is pretty damn big with a bastion of opportunities.
Bottomline, she's not going to float right into med school over you. But that doesn't mean her MIT school name doesn't give her an advantage. The key is that with great grades, great ec/recs and a solid MCAT, you TOO can go to a great med school. You have to earn it, just like she will.
good luck, and try stop worrying about your friend at the big-name school.
