You would need to clear up your record in NC. Why are you being told that you are not eligible?
"Arizona is a member of the Interstate Drivers' License Compact, any information about DUI arrests in other member states is shared. The only states that are not part of this compact are Georgia, Massachusetts, Michigan, Tennessee, and Wisconsin."
"Expungement if Convicted of DWI
If you have been found guilty of or plead guilty to a DWI, you can now seek an expungement, but the process is much more difficult. In fact, until just a couple of years ago, you were unable to do anything to expunge a DWI off of your record. However, the General Assembly passed a law (North Carolina General Statue 15A-145.5) that now permits a DWI (and other types of crimes) to be expunged under certain circumstances. First, the conviction must be more than 15 years old. The law also requires that any term of punishment also must have been completed 15 years ago. So if you were convicted 15 years ago but got one year of probation, you would have to wait until your last day of probation is at least 15 years past before you can apply for an expungement. Secondly, you cannot have any other conviction for a felony or a misdemeanor (other than a traffic violation) on your record. And, finally, you will have to go through the legal process and pay all required fees to have the conviction expunged. After you apply for an expunction, the necessary paperwork must go through all the county and state agencies that have a record of the conviction. Although the publicly available records will be expunged, you can expect confidential files to be retained. The expungement does not erase all record of your prior conviction, only what can be found by routine background checks and criminal record searches." http://www.mecklenburgdwi.com/nc-dwi-penalties/nc-dwi-expungement/
Do you meet the criteria?