How effective is a diploma from a target school?

Hello everyone! 

I'm an HS freshman in the NY area, and I've been interested in getting into investment banking. 

For pretty much all of my life, I've been hearing from my parents that going to an HYSPM or a tier-1 school is the be-all and end-all of how well my entry into the workforce goes. Unfortunately, I've only started getting my shit and work ethic together recently, and though my parents and socioeconomic privilege have carried me into a top-tier private high school, there is a massive distance between where my application is right now and where it needs to be in two-ish years. 

I honestly don't know whether I'll be able to make it into a good enough college in that time, and I'm worried that my past mistakes are going to screw me over later in life. 
I wanted to ask people currently employed in the industry whether there's a big difference between a tier-1 college junior/interviewee and a tier-2 college junior/interviewee in skill level and hireability, and if the college you go to is frequently referenced for promotions, exits, etc. 

Thank you!