No.
If it's important stuff or just getting her somewhere faster, or safer, than alternative modes, hey that's good brother stuff there. If you're just at her beck-and-call for crap that she can/should have taken care of herself, not so much a requirement. If you do and she's grateful, that's incentive to you to to it more. If you do and she isn't grateful, well, you aren't obligated to it.
This is a phase for younger siblings, because you have a privilidge, they feel entitled to it as well. It usually passes, or at least it used to. The yonger end of the teenage spectrum isn't what it once was. Generally speaking, she isn't going to hate you for it the rest of her life.
As for the comment about parenting her as a sibling, with discipline and re-inforcment, no. That is not your place. Older siblings are role-models and mentors growing up, at best. The end.
I'm going to base an "if" situation on an assumption that you're free to clarify. If you're in school in the U.S., I'm going to assume that you don't fully pay for the costs of your car. If your parents are granting you the privildge of using something that they pay for, you should also accept the responsibilities. Ask them, they make the call of what you respond to for her, because if it wasn't you, it'd be them.