I found this from a thread on another site regarding parasitic diseases. I believe what you have is a parasitic copopod.
They call them anchor worms, they are common on firefish, especially purple ones. Its probably bugging you more than it is him, but if it is in his gills it could eventually kill him. You can treat him a variety of different ways. You can net him and physically remove it with tweesers if its on the body but I wouldn't do that if it was on his gills. You can use any of the dips or quarantine him and use copper or Green X. You have to be careful not to over treat him with these treatments, gobies tend to absorb the chemicals through their skin and become toxic quicker than other fish. Just follow the instructions and watch him. You can bring the salanity real low to about 17 or 18 (that will kill invertebrates do it in a treatment tank) You also would run the temp about 82 and crank your ORP to between 450 and 500 (if you can) You have to watch him for infection in the gill , if so use erythromyocin. if you can't get him out the reef tank, you can use GreenX, I know Terry doesn't like it, but I have used it a lot with good success. You gave to remove any carbon filters and shut your skimmer down for about an hour after applications. I use it sparingly and it effective on the ich and other parasites. You can follow the instructions or cut back the dosage some if you have sensitive corals, the stuff is poison. I have a large crown that don't like it too much, they will close up but come baxk nice after the water is clear. Once you get rid of the worms or ich do a water change. Water changes are great my tank prefers more frequent smaller water changes, but they work miracles.
Hope this helps
