Rest assured. The only person who should be really embarrassed in this situation is your sisters friend.
Certainly, it may be a uncomfortable situation for you but If it will make you feel any better I am willing to bet your boy friend the police officer is not embarrassed by her saying he's dating her aunt because if anything his fellow officers will give him a pat on the back for (if it were really true) knowing shes related to you and still making the arrest anyways.
The only way this would be uncomfortable for him is if he didn't make the arrest and she later told someone he let her go - thankfully thats not the case.
As someone who works in law enforcement my self I know that people will say or try to do anything to get out of the situation they got themselves into. As a alcoholic myself, i also know that officers do try to keep their lives private but as long as they are doing their job and living a honest life there is little to worry about with his fellow officers. Best of luck to you and your continued sobriety.