To me it sounds like it could be an FPS issue. I see you tried changing the FPS via the options menu but there are a lot of different things that could cause your FPS to lock at a set amount. Verify your V-Sync is not enabled in Black Ops II, & Nvidia Control Panel. Ensure your FPS is not locked in Nvidia Control Panel as well. Run the command '/com_maxfps 250', and 'cg_drawfps 1' to troubleshoot and ensure you're at 250 (the ideal FPS setting for this engine).
I'll admit I'm no expert on anything else regarding this issue but framerate has caused me similar issues and I've since somewhat gotten familiar with it.
I hope this helps!