Yes a spectrographic analysis won’t show what’s going on with particles. Anything you can see is way too large to be analyzed by the ICP. In fact, the machine is protected against such particles.
Considering what you are seeing in that sample I would opt for a test that either does some pre-processing on the sample (such as an acid digestion) or a different test such as SEM-EDX.
Unless you are absolutely sure that you were introducing the particles during sampling. But I would not be so sure if it were me.
Either way this is a pretty good illustration of the limitations of emission spectrography. Those particles are there yet you said the analysis came back fine.