They are all correct in different situations. They show the difference between having a stomach ache and starting to have one, as well as different tenses. However, you are missing the main and most neutral version: I have a stomach ache. About the other versions: I have got a stomachache. = 1. An alternative or UK way to say 'I have' a stomach ache. 2. The moment that you start to have a stomach ache, described in Present Perfect (UK). I have gotten a stomachache. = The moment that you start to have a stomach ache, described in Present Perfect (US). I had a stomachache. = I had a stomach ache in the past, described in Past Simple. You don't have it anymore now or in your story. I got a stomachache. = The moment you started to have a stomach ache, described in Past Simple.