If you want to continue seeing this guy then you have to understand that because you drunkenly made out with his cousin, someone in his family or someone who saw you making out is going to tell him. That means you have damage control to do.
It’s much worse if he finds out without your telling him, so fess up and apologize, and do something about your excessive drinking so you don’t sabotage important relationships because you’re inebriated.
I hope that helps. Please follow me @AskAprilcom on Twitter.