Prince Jackson Life Goes On

6/12/2013 6:30 AM PDT

Prince Jackson -- Life Goes On After Paris Jackson's Suicide Attempt

Prince Jackson clearly knows how to compartmentalize his life ... because he hit the town Tuesday night in low fashion, attending the premiere of True Blood, Season 6.

The 16-year-old and his GF, Remi Alfalah, were flanked by 3 bodyguards as they left the ArcLight in Hollywood. 

People inside the screening tell us ... they were "touchy-feely" and seemed happy.   Almost everyone was dressed up -- except Prince, which either makes him a slouch or a baller.

Prince seemed annoyed when photogs asked him about his sister, Paris ... specifically how he felt about the possibility that Debbie Rowe could become her guardian.