Stringent line-of-sight demands necessitated by the fast attenuating nature of millimeter waves (mmWaves) through obstacles pose one of the central problems of next generation wireless networks. These mmWave links are easily disrupted due to obstacles, including vehicles and pedestrians, which cause degradation in link quality and even link failure. Dynamic obstacles are usually tracked by dedicated tracking hardware like RGB-D cameras, which usually have small ranges, and hence lead to prohibitively increased deployment costs to achieve complete coverage of the deployment area. In this manuscript, we propose an altogether different approach to track multiple dynamic obstacles in an mmWave network, solely based on short-term historical link failure information, without resorting to any dedicated tracking hardware. After proving that the said problem is NP-complete, we employ a greedy set-cover based approach to solve it. Using the obtained trajectories, we perform proactive handoffs for at-risk links. We compare our approach with an RGB-D camera-based approach and show that our approach provides better tracking and handoff performances when the camera coverage is low to moderate, which is often the case in real deployment scenarios.