I fixed this! I went into my router's advanced settings and turned on port-triggering (not forwarding). See screens:
First thing I did to resolve this issue was, join a game. Then I opened Task Manager by right clicking the taskbar. If you have not done so already you may need to expand in order to see all tabs/details. Find the APEX Legends in the Processes tab. Right click and go to details. Get the number in the PID column. You may need to add the PID column if it does not show up in the details tab. Using that PID in either command prompt or powershell enter the below where after FINDSTR is the PID for your running APEX legends. You will probably have more results. What I found in common on both computers on my LAN were TCP/3216, UDP/37005, UDP/37015.
As with other suggestions now log into your router and configure port triggering. I did not have to set up any port forwarding. I created three services, 1 for each port and enabled for all devices.
PS C:\WINDOWS\system32> netstat -ano | FINDSTR 12796
TCP 127.0.0.1:39237 127.0.0.1:3216 ESTABLISHED 12796
UDP [::]:37005 *:* 12796
UDP [::]:37015 *:* 12796
wtf is this
