The Internet of Medical Things (IoMT) is a rapidly growing field that requires efficient methodologies for network management and data handling, coping with the increasing quantity of data related to healthcare and medical services. Existing approaches to IoMT network management suffer from dynamic traffic, node-to-node communication reliability, and efficient data handling, which lead to increased latency and reduced throughput in the IoMT network. This work presents a number of innovative approaches with deep learning and optimization techniques to handle these limitations, enhancing IoMT network efficiency and reliability. We first propose a dynamic learning-based routing protocol using a Deep Q-Network (DQN). This method uses reinforcement learning to dynamically adjust the routes based on the realtime condition of the network, such as traffic load and reliability of node-to-node communication. The use of DQN means the network will be able to learn and adapt to the conditions continuously and hence will reduce latency by up to 20% and could increase the packet delivery ratio by about 15%. We then use Long Short-Term Memory (LSTM) networks for predictive analysis in traffic management. LSTMs make use of past data of network traffic for predicting future conditions, which may improve traffic flow and lower congestion. The accuracy of traffic prediction is expected to be around 90%, which can significantly increase network throughput and reliability. Our third approach uses graph convolutional networks for network graph analysis to optimize routing paths. We process graph-structured data in which features from node neighbors are aggregated to learn complex patterns in a network. We expect a 25% improvement in throughput efficiency in the network. Complementary to all these neural network-based methodologies, we will be using the tool NS2, a modular network test environment for simulating and emulating IoMT scenarios. This tool is of great importance in proving the improvements from our proposed solutions under controlled, realistic conditions. Lastly, data-driven decision-making is done using Bayesian optimization within the IoMT framework, especially for the tuning of machine learning model parameters. This optimization reduces the time spent on the model tuning to 50% and improves performance metrics by 10-20%.