Sounds like you're on the right track with the meds then and also sounds like they need it. Things to look for (and you probably have seen, but haven't noticed):
1) White, stringy poop <-- Internal Parasite/Bacteria
2) Clamped fins <-- Usually an end stage of some disease. Typically not a good sign
3) Red streaks in the fins <-- Usually comes with an internal infection of some sort and is usually the end stages. Typically not a good sign. Of three instances I've seen this, all three fish have died within a couple of weeks. Can also be from ammonia toxification.
4) Dropsy <-- Hard to cure in goldfish, if not all fish. Scales will stick out like a pinecone due the body bloating. The bloating is often from the internal bacteria/parasite that is turning the inside of the fish to liquid or shutting down of the kidneys.
5) Pop-eye <-- Often comes with dropsy, but alone it can be cured. Of course, if you have a telescope fish (like a moore), then this may be normal or hard to spot.
6) Inflammed gills or anything of the sort (like you're already aware of) <-- this can be a lot of issues, but namely flukes and toxification. Flukes will come with flashing.
7) Little-to-no-movement; like laying on the bottom for lengths of time <-- This can be a sign that the fish is ready to pass, but more so when the fins are clamped. It may also mean that he is just tired, which could be due to lack of oxygen, toxification, stress, etc. This is a hard one to diagnose. In fact, one of my oranda's stayed at the bottom for nearly 2 weeks when introduced, yet he looked fine, didn't have clamped fins, ate, etc. He was just getting use to the new home. On the 3rd week, he was out and about.
8) Gasping at the surface <-- Goldies can get air from the surface, but it's not the best for them as it can lead to swim bladder disease. A cause could be stress, not enough oxygen, toxification, or a gill disease. Hard to diagnose.
9) Swim bladder disease <-- Fish will swim more odd than normal (fancies are already odd swimmers due to their deformation). Often, the standard pea feeding will fix this (due to constipation usually). If a steady pea treatment does not, then there really isn't much you can do. Serious (and rich) enthusiests have been known to perform surgery to place minute pieces of weight (rock) in the abdomen to try and correct the swimming.
Alright, I think I'm done for now. Those are the most common problems/diseases with goldfish to look out for. I've had experiences with most all and have cured just about all of them. Dropsy and the associated (red streaks) I have had a 0% success rate with so really keep an eye for this.
HTH!