[HELP] How do i create my own affiliate?

So I have a few friends with an online shop and i know alot of creators on social media with a huge following. And i thought about just saying [creator x] here is a product from [shop y] . tell your followers to use this coupon [creatx10%] and get paid for every bought item. (of course i will take a cut of it )
But if i wanted to scale this would be so hard and now i am looking for better way to do this.

is their a wordpress/jomla/etc. theme or plugin for that or do i have to get this custome made website ?

What is the online shop running as far as a CMS? There are tons of affiliate plugins for Wordpress as an example that would likely achieve the results that you are looking for without having to modify the existing site too heavily.