Lots of people end up in leadership positions that they aren’t qualified to fill. Those with innate leadership potential do the best they can, learn on the job, and ask for as much help as they can find. It’s not about winning awards - it’s about stepping up to a challenge and doing the best you can. I think that’s admirable and highly compelling - and it will take you along way in life. So no, don’t quit. And selective schools will want to hear about how you rose to the challenge, assuming you do.