Significant work has been done on advancing localization and mapping in underwater environments. Still, state-of-the-art methods are challenged by low-texture environments, which is common for underwater settings. This makes it difficult to use existing methods in diverse, real-world scenes. In this paper, we present TURTLMap, a novel solution that focuses on textureless underwater environments through a real-time localization and mapping method. We show that this method is low-cost, and capable of tracking the robot accurately, while constructing a dense map of a low-textured environment in real-time. We evaluate the proposed method using real-world data collected in an indoor water tank with a motion capture system and ground truth reference map. Qualitative and quantitative results validate the proposed system achieves accurate and robust localization and precise dense mapping, even when subject to wave conditions. The project page for TURTLMap is https://umfieldrobotics.github.io/TURTLMap.