"Justice is mine!" sounds like a better English translation. It's something one would say after getting retribution.
A couple questions: could one say "the right is mine", or would that be "dreptul este al meu"? Also, while I understand that this means "justice is mine", could it also be interpreted to mean "I am correct" as in "am dreptate"?
That would be "dreptul este al meu".
As for your second question, I guess that given a proper context, you could interpret it as "I am correct", but it seems a bit far fetched.