Goldfish

A few months il y a my family and i went on holiday and my 4yr old son won a goldfish off a stall we called Goldy, hearing we had a goldfish a friend of ours offered us hers called Russ as she was unable to care for it any longer so we bought a 15 gallon tank that we were told would be big enough for two.
They lasted a few weeks until i realized Russ was looking a bit under the weather, took some photos and was told par a pet boutique owner he had nitrate poisoning and gave us some water treatment, he told us to keep Goldy in with him as he was plus the likely affected too, so there was no point isolating either one. The water treatment failed and both died, needless to say my son was heartbroken. We shut the tank down, cleaned everything out, gave it a good wash and set it back up again, three weeks later we went to get two more. Another orange fantail, and this time an Albino one which we were told were compatible. I had a good look and neither seemed to have any problems. We've had them less then a week and two days il y a the lamp on the fishtank went out and we haven't been able to find a replacement. They live in the kitchen, so we've been keeping an under the cabinet lamp on near the fishtank to be on the sûr, sans danger side.
But now the albino poisson is looking lethargic, twice he's been stuck in the model house and i've had to remove it to stop him from suffocating and he has white spots on his body and tail, almost like dandruff. What is it? Is he infected ou is it something to do with the tank and the pump?