Many of the answers below tell you to either (a) suck it up, or (b) break out of what seems like jail. May I suggest a compromise? You do need to talk to your Mum, but don't do it in a confrontational sort of way, as more than one person below has suggested, to "lay it on the line". Any good negotiator will tell you that is *not* the way to earn respect. And no matter if you're a really wonderful daughter or not, you know that what you're really talking about here is to earn respect as an adult.
If you're telling the truth, that you've done nothing to earn being what you think is being treated unfairly, then I suggest you put the ball in her court, with a simple first step. Getting a job to save for college is a worthwhile goal, so ask her exactly what you need to do to be allowed to get a job. She's then forced to be very specific, and give you certain conditions. As long as you meet the conditions, you've both had a "win", and there is no loser in the situation. The job is only your first step to earning more and more freedoms. Demonstrate to them that you're doing what you say you're going to do, that you're home on time, not forgetting to do your regular chores, etc., and after a few weeks, ask for another freedom.
Several people below have also suggested that a little lie now and then won't hurt anyone, to tell your parents that you were working when you were instead out with friends. I would say that this is a very bad idea, as it would break the trust that you're working to build with your parents. If they found out (and they always do, don't they?) then any headway you've made will be a complete waste. You'll never be given any privileges again.
As for complaining about chores, yes, often girls are given more chores than their siblings, especially if they're the oldest, which I was. I would say that you're basically stuck with that. But what doesn't kill you builds character. (Yeah, I know. I would hate it if somebody told me that too, but it's true. Sorry.)