Red spots on goldfish could be an indicator of an infection or parasite, and prompt treatment. Antibiotic medications are usually the best solution, however tailored specifically to each strain of bacteria; an aquatic veterinarian will be invaluable here, performing tests and suggesting the appropriate medication.
Red spots on goldfish may be caused by ammonia levels reaching above ideal due to overfeeding or inadequate tank filtration, and water test kits are an invaluable way of detecting whether this situation exists in your aquarium. In case of poisoning due to ammonia exposure, immediate large water changes must occur: change out all old water for clean unchlorinated freshwater with temperature-matching temperatures; alternatively if the tank is too small for full changes then treating infected goldfish in separate bowls is more suitable.
Labored breathing can also indicate a bacterial infection and is typically caused by Aeromonas bacteria found throughout aquatic environments. An infection often leads to listless swimming, reduced appetite, and clamped fins as symptoms.
Fish dip designed for treating bacterial infections could help your goldfish overcome red spots on its scales, including Nitrofurans and Sulfonamides, both proven treatments. Follow manufacturer's instructions when mixing your medication and dip the fish for at least an hour each day until red spots have vanished from its scales.