I'll try to come back and edit my answer when the question is updated (see "updates" below!), but here's a start:
Given the family situation you mention, you might need to ensure (or keep) her trust. Show her that you're able to keep things separate -- her achievement is not lessened by her stealing, but rest assured that the stealing will be dealt with too! I would try to deal with this as two separate things, at two different times. So:
First, you promised your sister a prize if she achieved a goal. She has earned this and you should keep your promise. Also, adjust your expectations so that your next challenge to her is a real challenge. You could praise her for (positively!) surprising you.
Second, the stealing. This is serious. Your question doesn't explicitly say from where she stole the goods but I will assume that she stole it from a store, not from your room. This is a criminal offense, and no small value, either! If she had been caught, she'd be facing problems. Serious problems. With "The Law."
Before you punish, learn her point of view:
Explain that stealing is never okay - ever. Ask her why she did it. Figure out what her motivation was. Was it just for fun? Does she feel pressured by peers to have these items? Did she steal because she wanted the items or because she wanted to do the deed?
Learning her motivation is important because you can't adjust behavior if you don't know what causes it. Once you know this, seek her cooperation to think up other ways to achieve what she wants. Be constructive, helpful. Next time she wants (whatever), get her to tell you and then you can make a plan together -- perhaps she can ask you for another challenge so she can earn some money, or do some extra house chores for money.
Now that you've given her a "way out" in future situations, it's time to look at her crime. It's time for punishment!
Does she understand that she did wrong? That she should not do it again? That she will get caught? (Hopefully by you and not by law enforcement!) What punishment does she think is appropriate? Maybe you can work out a settlement - something that certainly is a punishment but perhaps a milder one than you'd have chosen, but she gets some credit for admitting the crime and for working out a punishment. This discussion will tell you whether she has understood the gravity of the situation, and you can adjust your response accordingly.
Finally, once a punishment is announced, enforce it. Make sure she doesn't walk away from it and if she does, punish for that.
One threat you might choose to use is that if you ever catch her stealing again, you'll walk her to the store manager and have her confess. Depending on the crime, and the mood of the person you speak to, this can result in a slap on the wrist, or actual charges. Be careful.
You should give her back the $100 that she earned from you. You demonstrate good personality traits especially when it's against your interest to keep your promise. Notice the comments by deworde and Beofett!
Stealing from a store:
Does she realize just how merciful that store manager was? She could have gotten into life-altering trouble from that. It would be a valuable experience for her to go back to the store manager and thank him for how he handled it! And, of course, she also needs to apologize sincerely.
She doesn't seem to have understood her fault, or doesn't understand that actions always have consequences. As the saying goes, "when you pick up one end of a stick, the other end always comes with it."
Criminal offenses are much worse than putting a dent in mom's car, or eating a sibling's candy. Make your best effort to explain why her suggested punishments aren't appropriate, and then explain why (insert your suggestion) is a suitable punishment. Listen to her complaints about your suggestion and pick her arguments apart with logic and reason.
Because you're not her mother, I can't know how much authority you really have, so adjust your suggested punishment to the level that you can personally enforce.
I realize that we don't know her age, so perhaps she's really too young to grasp how big her mistake was. But I'm thinking that if she were that young, she wouldn't have stolen makeup. Perhaps I'm guessing poorly.
Lastly, remember that it's incredibly easy for us Internet strangers to sit here and type out what one could/should/would have done. Actually being in the situation, and having to think up perfect responses, is difficult. Whatever happens, please don't be too hard on yourself. You're making great efforts to handle this well, and that's absolutely commendable.