The only disease I know of that causes small black spots on fish is black spot disease (Diplopstomiasis).
Try deworming the fish withPraziquantel or Flubendazole.
Remove carbon from filters before treatment and increase aeration/ surface turbulence to maximise oxygen levels in the water.
You treat the fish once a week for 4 weeks. The first treatment will kill any worms in the fish. The second, third and forth treatments kill any baby worms that hatch from eggs inside the fish's digestive tract.
You do a 75% water change and complete gravel clean 24-48 hours after treatment. Clean the filter 24 hours after treatment too.
Treat every fish tank in the house at the same time.
Do not use the 2 medications together. If you want to treat both medications in a short space of time, use Praziquantel on day one. Do a 75% water change and gravel clean the substrate on day 2 & 3. Treat the tank with Levamisole on day 4 and do a 75% water change and gravel clean on day 5, 6 & 7 and then start with Praziquantel again on day 8.
The water changes will remove most of the medication so you don't overdose the fish. The gravel cleaning will suck out any worms and eggs that have been expelled by the fish. Repeating the treatment for 3-4 doses at weekly intervals will kill any worms that hatch from eggs.