Ok lets start here. What ever it is , is prob still in the tank. I would get the qt going and keep it going incase u need it for the goby. This is my option, but if u need/ want to treat the goby I would use a copper based med, bc its a wide spectrum killer of nasties and your unsure what your dealing with.
Now to your invert question. Generally no fish diseases dont effect them, but fish meds will, so dont treat a tank w them in it. Should u qt them. If u want the safe answer yes! Not many people do. I do not, but iam anal where I buy mine from and there only kept in invert tanks no fish.