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First, I can't get an appointment with a vet because they are not in today, but I will be taking him tomorrow.

In the meantime, I am worried that he has a parasitic infection. Cleaning the tank, I found small black worm-like things. He has not had a great appetite lately and now began to throw up.

Is there anything I can do while I wait to get into a vet?

What do you normally feed him? What was it that he threw up? Try to collect samples of those worm things for the vet to examine. Is there fish in the tank?

The worm thing might be a planarian. They show up when there's excess food/waste in the tank.