Red spots usually indicate a bacterial infection or irritation from dirty water. Sometimes it is both. Goldfish tend to produce a lot of waste, more so than most tropical fish in an aquarium. Make sure your tank size is large enough to help dilute the waste produced by your goldfish and that you are doing regular partial water changes.  Also check your water filter to see if it's working properly.

It could also be septicemia, which is a blood infection possibly caused by bacteria. Some of of the symptoms septicemia are red spots or rashes , becoming lethargic and losing interest in food. Some medications that are effective against this type of bacteria are Maracyn TC, Fish Cycline, Maracyn + Maracyn 2, Furan 2 and Metronidazole.

It could just be the coloring of the fish but I would try adding some sea salt to the tank for a few weeks just in case (one teaspoon per gallon)