The multimedia Tactile Internet is a network that provides ultra-low latency and ultra-high reliability for two-way multimedia services. Since random access in uplink dominates the delay and there exist variations of target delays among connections, it is much more efficient to perform a joint uplink and downlink resource allocation. In this paper, we provide uplink random access schemes with joint uplink/downlink resource allocation using multichannel architecture for multimedia Tactile Internet. By doing so, one can significantly increase the resource utilization efficiency and improve the reliability of the multimedia Tactile Internet as well. The cores of the resource management are two-fold. First, the joint resource allocation dynamically adjusts the ratio of the number of uplink channels and the number of downlink channels and performs access control based on the collision ratio and the queue lengths. Secondly, the efficient uplink random access increases the throughput, where each transmitting node selects a number of time slot/channel pairs based on either the Finite Projective Plane, the random numbers, or the hybrid. In the performance evaluation, we compare the performance of different selections for the multichannel architecture in terms of throughput for the multimedia Tactile Internet through simulation runs and analysis. The hybrid selection scheme performs the best since it has the advantages of both the Finite Projective Plane structure and being random.