Paddle faster Earl, I can hear banjos!
But seriously, there are issues here you should examine closely:
You're both young. very young, and this relationship may or may not wind up lasting. Now I know that there's the possibility you two are a match made in heaven, but the fallout with your family will likely be pretty permanent, even if the relationship isn't.
You're not related by direct blood, if I understand what you said about an adoption higher up the family tree, but you'll still be dealing with the social stigma of something considered strictly taboo in our society, and it's likely that's all acquaintances are going to see in you. Might make things tougher for you later on, if you two stay together.
Really, you might not even wind up liking each other, but you'll still see one another at family reunions and such. Constant exposure to one of your ex's can have a negative impact on later relationships, not to mention how a woman you're courting in the future might react to the news you were with your cousin.
If you absolutely must, if there's no going back, then go out on the DL for now, and if the relationship is successful for, say, two years(EDIT alright maybe that's a bit much but some nice time to see if this is the sorta thing that'll last. Six months, minimum.), then start talking about sitting down with your parents and giving them the scoop. No sense stirring up trouble if this falls apart after a week.
But if you have a choice at this point, get the hell out now, I've seen a series of events similar to what you describe go down and it got pretty ugly near the end.
Not that I'd suggest what you should do, one way or the other, simply that you should remember that it is ALWAYS going to make things hard. Of course, some loves are worth the effort...
