Cooperative relays improve reliability and coverage in wireless networks by providing multiple paths for data transmission. Relaying will play an essential role in vehicular networks at higher frequency bands, where mobility and frequent signal blockages cause link outages. To ensure connectivity in a relay-aided vehicular network, the relay selection policy should be designed to efficiently find unblocked relays. Inspired by recent advances in beam management in mobile millimeter wave (mmWave) networks, this paper address the question: how can the best relay be selected with minimal overhead from beam management? In this regard, we formulate a sequential decision problem to jointly optimize relay selection and beam management. We propose a joint relay selection and beam management policy based on deep reinforcement learning (DRL) using the Markov property of beam indices and beam measurements. The proposed DRL-based algorithm learns time-varying thresholds that adapt to the dynamic channel conditions and traffic patterns. Numerical experiments demonstrate that the proposed algorithm outperforms baselines without prior channel knowledge. Moreover, the DRL-based algorithm can maintain high spectral efficiency under fast-varying channels.