Will I not be able to get into good universities because of my grades?

I'm writing this from my cousin's account since I don't have one. I am 17 years old, from New Jersey, and I am going to be a senior. My freshman and sopre year of high school I did very well, but in these short 3 years, I have had problems with depression and social anxiety. I consider myself to be extremely intelligent, and I have rightful merits to be able to do so. I am taking AP Calculus BC and AP Physics this year in highschool, even though I have already taught myself advanced calculus and mathematics. I have always endeavored to pursue my studies at University of Pennsylvania, Columbia University, NYU, or Princeton; all local schools in the area where I could commute. As a forcibly clified high school student, I have been enduring a lot of distress over college. Due to my problems last year, I was out of school for many weeks, and missed many ignments. There were times I felt suicidal, and missed ignments like english quizzes and spanish projects. This really brought down my grades and as a result I had two C's last semester. I have perfect scores on my SAT, but now my gpa is low, and I won't even be able to bring it up by next semester of senior year before applying to colleges. I feel trapped because I do not have the required school "grades" to be admitted into an elite university, but the intelligence and capabilities. In my free time, I have been developing stochastic models, which have the possibility of being published. If I am isted in publishing some of my work, will the recognition of my capabilities help me get into the schools I want to pursue my studies at?