"When I got my driver's license in Miami..."
I had a similar situation, my lawyer said CBP will see the warrant but don't have time or resources to go through the hassle of extraditing you on a misdemeanor.
Since you bring up the license issue, your driving privileges are most likely suspended in all states. DUI laws have become so severe I was told I had to take the DMV
class on DUIs TWICE (in two different states) since the arrest was in Florida and the license was from California. Talk about screwy.