should an ordinary student give up?

I am currently a junior in high school, and to briefly summarize I have a high gpa (3.98). a high weighted gpa (4.42? i think), my class rank is 13 out of 500s (idk if thats necessarily amazing), and i have an average SAT score.
For the past couple of months, and probably my entire life I have always applied to things whether it be to run for secretary in a club or be a leader for a certain program. And not necessarily often but a lot of the time, I get rejected for a better student. And honestly, I am truly just wondering if the same thing is going to happen with college admissions. There is always going to be a better student, my ec’s aren’t anything short of ordinary, I may have unique background but how far will that ever take me?
I always dreamed of going to duke or georgetown, but i feel as though if i have failed so many times with a smaller pool of students how would i be able to compete against thousands?

do i even have a chance

You sound pretty discouraged, though I think it’s partly from a lack of confidence. Be confident! Nobody knows for sure they’re getting in anywhere, they just do their best and put their best foot forward. I advise you do the same and just keep trying to do well in school and pursue what you love. Your stats will not be a problem (depending on your SAT score) and if you have unique circumstances or ECs, talk about them! I would advise applying early, as that gives you a pretty palpable boost in your chances. I’ve seen some crazy things this application season in terms of who got in somewhere and who didn’t. It’s all a crapshoot, so just make yourself look as good as possible and put yourself out there! And by the way, if you portray yourself as someone who thinks they’ll never get into Duke, i can guarantee you never will, so believe in yourself:).

A named position in a club isn’t what colleges are looking for. Put your energy into contributing. Organize something, volunteer someplace unusual, be a top team player in an EC (Quiz Bowl, Robotics, debate, etc). Strike out more in a direction that is unusual.

If you don’t try, you’ll never know. The most important thing is having a “narrative” in your application. You said you have a unique background. Try to tailor your app around that!