There are loads and loads of people who have intimate relationships with their first cousins. There are loads of websites on it too. I think one is called Kissing Cousins or something, I saw it years ago.
Now, every person (well, adult) is entitled to do what they want with their lives. Zack, without being patronising, you are still young, and one day, you will look back at this situation and you may laugh, cry, find it amusing, horrible, even revolting, whatever. Or you may be with your cousin. But whatever happens, remember that what you do will ahve consequences.
I personally don't think its a good idea to ahev that kind of relationship with your first cousin, for reasons mentioned by others here, eg genetics etc, but I think your r/ship has not gone so far as kids so I won't go onto that.
Just think carefully before you do things, its very easy to get carried away and emotionally involved with someone, anyone, at the moment but later you may regret it. At the end of the day, whatever you do will be part of your experience growing up and it may teach you about yourself. I would advise, leave that kind of relationship to non-relations as opening up that can of worms can lead to a lot of heartache and family problems. Whatever you decide, good luck and try to be mature.