The millimeter wave (mmWave) bands are likely to play a significant role in next generation cellular systems due to the possibility of very high throughput thanks to the availability of massive bandwidth and high-dimensional antennas. Especially in Non-Line-of-Sight conditions, significant variations in the received RF power can occur as a result of the scattering from nearby building and terrain surfaces. Scattering objects come and go as the user moves through the local environment. At the higher end of the mmWave band, rough surface scatter generates cluster-based small-scale fading, where signal levels can vary by more than 20 dB over just a few wavelengths. This high level of channel variability may present significant challenges for congestion control. Using our recently developed end-to-end mmWave ns3-based framework, this paper presents the first performance evaluation of TCP congestion control in next-generation mmWave networks. Importantly, the framework can incorporate detailed models of the mmWave channel, beamforming and tracking algorithms, and builds on statistical channel models derived from real measurements in New York City, as well as detailed ray traces.