Translation:He could have gotten chest pain, if he took the wrong medicine.
"Gotten" is not just an Americanism - it's also Old (and Middle) English. It went to North America with the English emigrants in the 17th and early 18th centuries, whilst it disappeared in British English through the 18th and 19th centuries. It remains standard American English, so is just as acceptable a form as "got" in standard British English (though "gotten" seems to be coming back to Britain as well - a lot of young people here use it).
I understand what you say but the same argument could be made for Québec French or for Afrikaans (in relation to Dutch). The Oxford Dictionary lists it as 'North American usage'. But even other words through this course, like 'sucky' or 'fall' (instead of autumn) are chiefly American, that's why I felt the need to comment on them.
Either way the main point I wanted to make is the one made above, by yourself as well, that it should be in the Third Conditional form 'had he taken/if he had taken', and not the Simple Past 'took' =)