Over the last decade, there has been increasing interest in autonomous driving systems. Reinforcement Learning (RL) shows great promise for training autonomous driving controllers, being able to directly optimize a combination of criteria such as efficiency comfort, and stability. However, RL- based controllers typically offer no safety guarantees, making their readiness for real deployment questionable. In this paper, we propose SECRM-2D (the Safe, Efficient and Comfortable RL- based driving Model with Lane-Changing), an RL autonomous driving controller (both longitudinal and lateral) that balances optimization of efficiency and comfort and follows a fixed route, while being subject to hard analytic safety constraints. The aforementioned safety constraints are derived from the criterion that the follower vehicle must have sufficient headway to be able to avoid a crash if the leader vehicle brakes suddenly. We evaluate SECRM-2D against several learning and non-learning baselines in simulated test scenarios, including freeway driving, exiting, merging, and emergency braking. Our results confirm that representative previously-published RL AV controllers may crash in both training and testing, even if they are optimizing a safety objective. By contrast, our controller SECRM-2D is successful in avoiding crashes during both training and testing, improves over the baselines in measures of efficiency and comfort, and is more faithful in following the prescribed route. In addition, we achieve a good theoretical understanding of the longitudinal steady-state of a collection of SECRM-2D vehicles.