A cruise at that time of year should have lots of young adults your age. Sometimes they will post specific gathering points for teens and do try to treat the post-HS group a little differently. Carnival realizes you don't need/want a bunch of camp counselors.
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014, 2016
Sail Windjammer: Mandalay 2017
Star Clippers: Royal Clipper 2015