In 3GPP New Radio (NR) Vehicle-to-Everything (V2X), the new standard for next-generation vehicular networks, vehicles can autonomously select sidelink resources for data transmission, which permits network operations without cellular coverage. However, standalone resource allocation is uncoordinated, and is complicated by the high mobility of the nodes that may introduce unforeseen channel collisions (e.g., when a transmitting vehicle changes path) or free up resources (e.g., when a vehicle moves outside of the communication area). Moreover, unscheduled resource allocation is prone to the hidden node and exposed node problems, which are particularly critical considering directional transmissions. In this paper, we implement and demonstrate a new channel access scheme for NR V2X in Frequency Range 2 (FR2), i.e., at millimeter wave (mmWave) frequencies, based on directional and beamformed transmissions along with Sidelink Control Information (SCI) to select resources for transmission. We prove via simulation that this approach can reduce the probability of collision for resource allocation, compared to a baseline solution that does not configure SCI transmissions.