How do I clear up a two year old DUI?

You will have to appear in court or appear through an attorney.

You have an arrest warrant. To handle a warrant, you must turn yourself in to the issuing court, with or without an attorney. On misdemeanors like DUI, an attorney can appear in court without the defendant being present which is safer and avoids immediately being taken into custody. You'll try to negotiate a recall of the warrant[s] and bail reduction or OR release. You'll try to negotiate a plea bargain on the Failure to Appear charge that caused the warrant. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. Effective plea-bargaining, using whatever legal defenses, facts and sympathies there may be, could possibly keep you out of jail, or at least dramatically reduce it. Unless you're competent to effectively represent yourself in court against a professional prosecutor trying to put you in jail, most people hire an attorney who can.