I applied for public housing and section 8 they told me i am not eligible because i am an adult living with my mother ?

Section 8 is awarded based on the household and the income shared by the household. If you live with your mother and she owes rent to public housing, you are part of the same household and one of the beneficiaries of her award. As a recipient of this privilege, she is required (generally) to pay 30% toward the rent and the rest is covered by the service. You have benefitted from that while living with her, and now she has allowed an outstanding balance to accrue. Your application for the same benefit appears to be an attempt to side-step the payments she owes by qualifying for the same benefit on your own without helping pay your share: with every benefit comes a responsibility.