Hi xoxot, welcome to the site.
As Serendipity has inferred, you need to look at what you are risking. I doubt very much that your parents will be easily won over to your point of view. They are still going to be very sore that their adult nephew was messing with their juvenile daughter. Any decent, loving parent would be.
You mentioned that you are hoping to start college soon. Don't let this relationship override that. A good education is your insurance if things don't work out and you have to support yourself. I suggest you put your relationship with your cousin on hold until you complete your education. If he's sincere about you, he'll allow you to do that and wait for you. if he's not cool about it, then he's just being selfish, and you're just another piece of ass to him.