Chill out. You're not going to get anywhere fighting the system. Work with what you've got. If there's any non-science professor you've enjoyed and thought a friendly sort, reach out to them and explain your situation. Set up a meeting so you can talk with them about medicine and your aspirations. One thing a lot of students forget is that professors are people too, and they recognize unfortunate situations when they see them. Many are there because they love teaching and helping students, and they want to help you succeed. Yes, it may not be the pinnacle of all reccomendations, but it will get you where you need to be.