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On that series, QoS does support two ingress queues toward the fabric. In theory, I believe you could prioritize certain ports and/or VLAN traffic, but I wouldn't recommend it, for two reasons. First, the two queues are really to allow critical timing depending traffic priority, e.g. VoIP, and second, these queues are unlikely to congest except perhaps on the original generation 3560Gs with 52 gig ports. Congestion is also possible on the 3560Gs with 24 gig ports. It shouldn't be an issue on the 3560 with FE ports, or the -E or -X series.
Much more common on 3560s is congestion on an egress port. 3650 support 4 egress queues, although default buffer allocations often result in egress drops for bursty traffic, which might be mitigated with buffer tuning. So, again, you could prioritize certain ports and/or VLAN traffic.
