Small cell densification and advanced multi-user access schemes are promising approaches to dramatically improve 5G system performance. Towards efficient spectrum usage in ultra-dense heterogeneous networks, spectrum reuse between backhauling and access links combined with full duplex is applied. This forms a full-duplex self-backhauled heterogeneous network (FS-HetNet). Considering co-channel interference caused by frequency reuse, and residual self interference due to imperfect interference cancellation in full duplex, interference management becomes a major issue in boosting network performance. In this paper, motivated by the emerging non-orthogonal multiple access (NOMA) for 5G, we consider a NOMA-based scheme to mitigate co-channel interference and achieve efficient spectrum utilization for FS-HetNet. We address an energy-saving problem for the considered network, aiming to satisfy all users data demand within a limited transmit duration by consuming minimum energy. In addition to the energy consumption in transmission, the consumed decoding energy due to signal processing in successive interference cancellation is also taken into account. We propose an energy-efficient and delay-constrained scheduling algorithm to jointly optimize transmit power, user clustering, and transmission duration. Numerical results demonstrate that the proposed approach outperforms previous schemes.