Frankly it seems completely unbelievable to me that a journal with an h- index of 31 (Nature , or Science) has taken on a 13 or 14 year old to do peer reviews.
Also, you mention that you got this position after two years of hard work. So you began doing publishable research at age 11?
However, if this is true, it is so extraordinary that of course you would not only list it, but write about it.
It also seems unbelievable to me that anyone smart enough to be doing peer reviews at internationally esteemed scientific publications isn’t also smart enough to know they should talk about it in their boarding school applications.