If you are turned 15 in July 2021, this means you are in the equivalent of UK Year 11, and if you were in a UK school you would be taking your GCSEs (or IGCSEs in your case) in summer 2022.
Anybody born between 1st September 2005 to 31st August 2006 is currently in Year 11, studying to take GCSEs in summer 2022
Anybody born between 1st September 2006 to 31st August 2007 is currently in Year 10, studying to take GCSEs in summer 2023
It sounds as though you were born in July 2006, am I correct?
This means, if you take your IGCSEs in summer 2003, you're going to be taking them a year later than usual, but it's not a big problem as you can still go to college straight after that.
Most schools do study the material over the course of 2 years though (over Years 10 and 11), so yes, if you're following the school system you should have already started studying by now if you want to take exams in summer 2023.
The good news is that it's entirely possible to catch up. If you want to get on track with the Year 11s for when you start at the independent school, start learning the syllabi now for each subject, and aim to be about half way through by the time you start school.
Get some textbooks and work your way through them.