Device-to-device (D2D) two-hop cooperative communication improves the network coverage and throughput to provide the quality of service and quality of experience to the end users. Nonorthogonal multiple access (NOMA) can be used at the D2D transmitter to improve the spectral efficiency of the network. But, two-hop transmission with NOMA suffers from delay and interference from the neighboring nodes. To resolve the aforementioned issues, in this paper, we propose Tactile Internet (TI) driven delay assessment for D2D communication (DIYA) scheme, which works in two phases. In the first phase, a full duplex communication at relays (intermediate nodes) is used to have the first- and second-hop transmission simultaneously in the same time slot. Then, TI-based communication is used at D2D transmitter to increase the speed of transmission. In the second phase, pricing-based three-dimensional (3-D) matching is proposed to improve the throughput of the cell edge users along with the mitigation of cochannel interference. Also, the power of the D2D transmitter is optimized using successive convex approximation with low complexity, which converts the nonconvex optimization problem of subchannel allocation and power control into convex problem. Numerical results demonstrate that DIYA achieves higher throughput with reduced delay in comparison to other existing orthogonal multiple access (OMA) and NOMA-based schemes.