Am I just being selfish by wanting to tell them?
First of all I don't think wanting your family and friends to know who really are can ever be selfish, you shouldn't even be concidering that.
Would we all be better off, and would they be happier, not knowing?
At first people can be difficult and not very understanding. But like other people have said you'll fell like a durdun has been lifted.
Does anyone out there regret coming out to members of their family?
I can't think of a single person that said they did.
All I can say is I'm sure you'll feel much better when they know, no matter how they react... you'll always be their daughter and they'll always love you.