First take care of your finger and next don't tell her to say sorry. Because most of the time they say it to satisfy you and don't even mean it. I'm sure she feels bad enough without punishing her, because most of the time it's not even effective. So depending on your sister age, she understands what she did, was not nice. I hope your finger gets better soon.
A human bite is full of bacteria. Please once you get it to stop bleeding (with direct pressure), you must keep it clean with peroxide. And some antibiotic ointment. Honestly, you may want to get it cleaned out by a healthcare professional.
A human bite has more bacteria, and much badder bacteria, than any dog bite. Since she bit you hard enough to draw blood, you should wash the wound with soap and warm water, then cover it with gauze or a soft towel. When your mother comes home, you must convince her to do two things: first, take you to the ER for a shot of antibiotics, and second, come home and bite your sister just as hard as she bit you.
When I was your age, my younger brother would not stop biting me, and it hurt horribly. Now understand that he was the golden child, and I was the red-headed step-child. Even so, my mother finally, as a last resort, took his arm and bit him as hard as she could without drawing blood. She had tears streaming down her face as she did this, but she still did it, and it worked. My brother let out a yell of surprise and pain, and he never bit anyone again.
Your sister must be tamed so she will stop behaving like a little savage, and become somewhat civilized. That is what parents are for; to tame the savage beast that all little children are, and make them fit to be among decent people. Your mom has a duty to do this, and you can tell her that I said so.