You're right that the issue is likely to be related to the USB-Serial bridge, but without seeing your schematic and board design no one is going to be able to offer any meaningful insight.
OP's pictures:For USB data lines, layout really matters. If you have a look at the official Nano PCB files you'll see that the USB data lines are as short as possible and of similar length. The traces on your PCB aren't so direct, and even include two superfluous layer changes on one trace while the other has no layer changes. You might need to redo that board if you want the onboard USB to work.