I have a network like

Node A to Vlan Switch
Node B to Vlan Switch
Node C to Vlan Switch
Node B is set up to be a middle man between A and C.
All nodes have 1 NIC.

They are all linux boxes. Node B can ping Node C. When I try to ping Node C from Node A, the ping just hangs forever.

When I use Wireshark to sniff What's going on with Node B during a ping from Node A to Node C, I can see an ICMP request with src = Node A and dest = Node C. I'd like to know if that ICMP packet was received by B from A or if it is going out. If it's going out, that makes no sense since B knows how to send to C. If B is only getting the requests but not forwarding them, then I know there is something wrong with B's configuration.

So I'd like to be able to sniff incoming packets only, or outgoing packets only. Is there a way to do this?

What Linux distro(s)? And can you provide more details about that network setup? All three are on the same vlan, and node B (with one NIC) is supposed to be a gateway between nodes A and C? (I don't understand the purpose.)

I don't have wireshark installed on my workstation, but you can quickly get this info using tcpdump(8) and its src net / dst net filter.

Example:
# tcpdump src net 10.5.5.0

Moreover, even without using such a filter you can determine how traffic is flowing by paying attention to the source and target (read from left to right) and the directional ('>') indicator.