@amtotheber210,
Are you and your sister naturally born from both of your parents?
Are you the same gender as your twin? If you aren't, then the answer is that you're not identical.
If she is your identical twin (and you're both female), if she has a different blood type then you're not identical? The answer is no.
"Since identical twins come from the same fertilized egg, they have the exact same DNA. They are always of the same sex and they have the same blood type. Testing the DNA of twins is one way to determine if they are identical or fraternal. "
I'll leave it someone else to tell you definitively whether or not about parental-child blood type difference possibilities. My guess is that ... yes, that you can have parents who are both B and you be an O type - because the O type is a recessive gene., but as I said, that's a guess on my part.