Does it mean a goldfish is sick when it doesn't move as much?

If the fish has warm enough water, with sufficient aeration and food, then it's probably not well. Goldfish may die after three years, so if your fish is that age or older, be prepared. I know it's hard to lose any pet , I still my Betta,Bruce, after two years, but it is natures'way, and it not realistic to spend hundreds of dollars on a$5 fish.If you see no discoloration of the scales, it's old age or an internal problem. I'm so sorry to not give you happier news.