Firstly, consider what you've lost compared with if she'd told the truth in the first place and offered you $9 full time. Did you turn down any other jobs that you'd have taken in preference?
If all you've lost is 6 days job-hunting, for which you've been paid, albeit 10% less than you expected, then this situation isn't all that bad. If the job you would have wanted turns out not to exist, you can just quit any time you like. If you wouldn't have taken the job for $9, then don't keep the job for $9 either.
Having nothing written down cuts both ways, she can hardly expect you to work out your notice. The best time to quit is probably when you've just been paid (because you're working for someone who is trying to cheat you), and/or when you've found another job. So ideally find another job, tell them you can start the day after your next payday, quit without notice once you have the money.
So, that's one option. Now think about what you've lost compared with if the job she described really exists, and you can take a shot at getting that. The way to do that is to go over her head, say that you were offered $10 and a guarantee of full-time work, and that if you don't get that (with back pay and in writing) then you're leaving. If you don't get it, leave, and learn a lesson about written contracts. Give them a very short time frame, you can't let them string you along while they delay.
Since she's the hotel manager, I expect it's pretty unlikely that corporate will do anything, although I don't know the hotel business. They have no evidence that you're telling the truth, they've barely even heard of you since you're a new employee, and even if they give you want you want you've still got to work for someone who you've humiliated. Therefore, it might not even be worth asking. But you never know, maybe you fit a pattern that they're already aware of.
Only if you've suffered substantial loss as a result of the deceit, and you can "prove" the loss and the details of the original offer, does the issue arise of whether this is fair or not. It isn't fair, but the fact that it's unfair doesn't help you unless you have a case to begin with (and maybe not even then, since a lot of things are unfair but legal).