If you mean by "got a DUI" that they charged you with DUI and you didn't go to court when you were supposed to go, the statute of limitations does not apply to you. The statute of limitations is time in which the state has to file charges (and in some cases serve you with a summons.) So if you go a ticket for DUI and the ticket or other charging document was filed, the case is a live case forever unless there are speedy trial or prosecution problems. if you failed to appear there is probably a bench warrant out for your arrest. If you are stopped for something in Arizona or somewhere else you can be arrested. When you go to renew your license it will probably be denied until you clear with Florida.
If you were not served with charges or went to court and found there were no charges, the statute of limitations may apply. There are rules about statutes of limitations and often the time you are out of the state does not count. You will need a lawyer to tell you and that lawyer will need to know details of the case that you should not post here,
In either case you will need Florida DUI counsel to clear up the problem. You can find counsel at the link below.