In reference to how the conviction appears on your record and what you were told, you should contact your AZ attorney to discuss that. As for how it will impact potential career opportunities, I would suggest contacting the licensing agencies for those you are interested and inquire. I doubt you would be barred from law school as long as you are honest and up front about them when filling out your application. Hope this helps. Good luck.
You've got a number of complicated questions that aren't easy to answer here. I suggest that you post this in the AZ section so some locally experienced DUI attorneys can advise you. While the DUIs shouldn't ultimately prevent you from getting into school, they will probably pose some complications upon graduation when attempting to get licensed by the state bar or medical board. Consult with a few AZ DUI attorneys to explore all of your options. Best of luck.
If you were represented by an attorney for one or both of thee charges, I suggest speaking to him, her or them as a starting point. A lawyer fully familiar with the facts of both of your cases is in the best position to answer your questions and assist you.
Good luck to you. And don't go to law school ... when you're done, you're a lawyer.