That's actually what happened to me with my first tank but sadly I stocked up on corals and inverts before the ich hit.
You have a couple things you could do.
1. Return any inverts and the piece of live rock you have with the coral growing on it (assuming you care if it lives or not) and perform a hyposalinity treatment on the entire tank.
2. Setup a second tank that you can keep the inverts and live rock in for 6 weeks straight without any fish while you do a 6 week hyposalinity treatment on the DT
3. Return the inverts and coral and treat the tank with a medication.
If you are sure that the fish has ich then there is really no way to know if your tank is going to be ich free or not a month or two down the road as one of the cysts might have already fallen off of the fish. Hyposalinity is the best way to treat ich but it has the downside of killing any corals or inverts. Here is a link to an article about treating it.
Marine Ich/Cryptocaryon irritans - A Discussion of this Parasite and the Treatment Options Available, Part I by Steven Pro - Reefkeeping.com