Which state's discovery rule and statute of limitation do I use for a personal injury case?

Without having more facts, it is difficult to give a specific answer. That said, assuming that the original injury (misdiagnosis) occurred in Michigan, while you were a Michigan resident, then Michigan's rules are likely to apply. Nevertheless, I would recommend checking with an attorney licensed in Alabama, especially if you are a resident of Alabama. Choice of law and statute of limitations questions are often complicated in these circumstances.