She would be around 6 months pregnant by now. I would question why you’re just now being told and I agree with the others. A paternity test immediately. Please learn from this if it is not yours. I’m glad that you’re willing to take responsibility though. Good luck!
I don't think there's anywhere in the US that having a relationship with a 3rd cousin (which is really, quite removed!) is a crime. Second cousins share one pair of great-great-grandparents. On the other hand, this is the teen pregnancy forum - you might get better discussion on the regular pregnancy forum, or on the DNA Paternity forum. Best wishes.
DNA testing, stat. And for god's sake, don't have sex with relatives.
Get a DNA test. This day and age, before you believe anything, you really need to be sure. If the baby is yours, yes, it's time to man up. Not only because you would be the father, but in the eyes of the family you would be doing something shameful if you don't.
Get motivated about your career, also. Fatherhood costs money. And, it probably goes without saying, stop having unprotected sex with anyone, cousin or not, unless you are OK on becoming a father.