I think the answer is

>! Riley

My prefix is called an island.

>! The island of [Rye](https://www.britannica.com/place/Great-Rye-Island), or the state code for Rhode Island, USA (RI).

My infix is an island.

>! ile, sounds like isle

My suffix is not so windy.

>! ley, not so windy as in "using or expressed in many words that sound impressive but mean little", indeed, it is very short.

I made this puzzle.

>! [Riley](https://puzzling.stackexchange.com/users/41566/riley), the first to drop [one of these types of riddles](https://puzzling.stackexchange.com/questions/62349/my-prefix-is-food-my-suffix-is-rude) here..