I mean, as a whole I agree that the plot is... lacking, to say the least, but, and I could be wrong, IIRC she didn't sell herself to the brothel, or at least, it was kind of a false choice
Their family owed the noble a shitton of money, but in the (admittedly fake) contract, he wrote in that, should their family be unable to repay him, they'd have to sell their daughter to make up for it.
Her two choices were (basically) to sell her to the noble himself as repayment, or to the brothel, to try and scrounge up the money that way and, as a bonus point, hopefully dissuade the noble by "soiling" herself. Except the noble ended up having his way by getting to her first, anyway. At least, that's how I remember it, after having re-read it recently.
Let's not look at things even worse than they actually are, especially since the writing isn't the best to begin with lol