Generally you are not allowed you to carry driver's licenses from more than one state at the same time. Indiana requires when you obtain an IN driver's license, for you to forfeit the license from the previous US state in which you had lived. Arizona likely has a similar rule, so having 2 licenses at the same time could get you in trouble.
If your licenses were somehow both valid, both Indiana and Arizona are members of the Drivers License Compact so out of state violations would be reported to your "home" state's licensing authority. It might be hard figuring out which is your home state in this situation.
Where your DUI is also very likely listed is the National Driver Register (NDR), which all states provide information to. The NDR is a central database of information on problem drivers. Problem drivers here are defined as though whose license has been suspended, revoked, canceled or denied or have been convicted of a serious traffic related offense (such as driving under the influence).
The state in which you are a resident of and your car is registered in, is more than likely the state in which you need your license valid in. You will also need the car insurance required in that state. You can get your cheap car insurance quote here with us.