What do your parents think about your cousin?
I don't really know your parents, but if they're anything like my dad, they probably won't want you dating other women, especially if you're bi. My dad is already pissed at me because I don't ever want to get married or have kids, it can get mighty hellish depending on your parents.
I just hate that homosexuality is such a huge target to so many religious people today. I'm religious myself, and it just baffles me to see so many people who misinterpret "these are the rules you need to follow" as "these are the rules you need to enforce
." I think many Christians need to convert themselves before trying to convert others, but that's just my opinion. Praying for others is fine (in a more "I'm praying they do the right thing" rather than "I'M PRAYING THE HOMO DEMON DISPATCHES AT ONCE"), sharing your religious beliefs is fine, but yelling "Y'ALLS FAGS GONNA GO TO HELL" to people who probably don't share the same beliefs as you isn't going to help anybody. I don't know why, but some people just seem to assume that their religious beliefs are 100% spot on, which is quite the dangerous assumption to have when many of life's answers can't even be comprehended by the human mind.
I'm not sure whether I'm on topic anymore.
Point is, you know your parents more than anybody. You should discuss this with someone you trust or share more information on your parents (as many of us might not have much to go on with the current information).
Also, therapist. Therapist therapist therapist. They'll give better advice than any of us.