Time-Slotted Channel Hopping (TSCH) is a medium access control technology defined by the IEEE 802.15.4e standard to address reliability and timeliness requirements of low-power Internet of Things (IoT) applications. Based on a communication schedule, TSCH exploits time-synchronization combined with frequency channel hopping to cope with wireless interference and multi-path fading. While standards define mechanisms for the basic configuration and communication of TSCH nodes, computing and adapting a schedule to the network and traffic dynamics are left as open research problems. In this paper, we propose a novel Distributed Traffic-aware Scheduling Function (DT-SF) for mobile IoT networks. DT-SF dynamically adapts the TSCH schedule to the changes of the traffic and the network topology. It estimates the node mobility by using a new lightweight approach and monitors the queue backlog to balance the traffic loads of children nodes. We model allocating TSCH timeslots to one-hop neighbors as a Mixed-Integer Convex Programming (MICP) problem which is solved by using the method of Lagrange multipliers and the Branch-and-Bound algorithm. We implement DT-SF on Zolerita Firefly IoT motes and the Contiki operating system to evaluate its performance on the testbed with 18 nodes. Evaluation results show that DT-SF improves the packet delivery ratio by up to 52% compared to the state-of-the-art method.