Help in finding out the truth - in NY

I recently found out that I may actually be the child of my cousin. I am 47 years old and I must say this is really giving my emotions a run for their money. I always knew that I was different from my family that I grew up with. I never really fit in. I do not know where to begin. My father, who may be my uncle, is the only one alive. He is suffering from dementia which creates much confusion. I did talk about the pregnancy and what he and my mother did to help; he refuses to talk about it. I have a certificate of birth registration that seems normal. I really want to know the truth and am not sure where to go next. Any help would be appreciated.