The fact that you got caught twice indicates that you made a habit out of drinking excessively and causing problems; it's different from a one-time thing. Also, both instances happened during your junior year, so the "I was trying to transition into college and things got out of hand" explanation wouldn't hold.
I think you'd need to take at least two or three gap years to dampen the effect of these mistakes, with lots of drug/alcohol rehabilitation volunteering. (Perhaps consider getting certified as a substance abuse counselor.)
In any given cycle, thousands of applicants will be just as academically qualified as you but have no red flags.