I think you're saying the Housing Authority paid your September rent, so that your payment of the September rent is an overpayment. If that is the case, you are entitled to a refund, and should ask your landlord for a refund. Small claims court is an option, but it takes a lot of time and steps. It may be easier to deduct your share of the rent from the overpayment, if landlord won't cooperate.
Section 8 adjustments are rarely, if ever, retroactive. If they fixed your monthly portion of rent to $5 in September, your october portion will be $5, not September. Think of it backwards. If your portion was $5 and section 8 changed it to $549 mid September, would you owe your landlord $544 more for September?
A proper response would require a thorough investigation into the history and background of this relationship. The information provided above is just that, information, to be used as you see fit.