I work that out to be only 12 gallons, i hope someone can confirm or give me a different gallonage.
if these fish have been in there for 4 or 5 years then i presume they wont be fully grown as they wont be able to grow properly?
at this age they should all be around 10 -12 inches long.
goldfish need around 20 gallons for the first fish and then an additional 15 gallons per fish after that.
i would suggest you either buy water tests for ammonia,nitrite,nitrate and ph or take a sample of both your tap and tank water (each clearly marked) to a pet store and get them to test it for you, asking them to write the values down for each water sample.
i dont know if the fish is sick because of poor water quality or it indeed has a swim bladder problem, but you will need to do more in the way of water changes to keep the water clean. i suggest doing 40% every 3 days and using dechlorinator to temperature matched water.
so for now stop feeding the fish and use the pea method above to see if that helps and keep an eye out to see what the poo looks like.
if one side is lumpy then that could mean a tumour, egg impaction or a deformity on one of its organs. as it comes and goes then i'm going toward egg impaction but could you get a pic of the fish and post it up?
you need a filter that turns over the water 10 times in every hour, so for your tank 120 gallon turnover is needed to keep you from doing all those frequent water changes. when cleaning the filter do it when you are not doing a water change and only rinse and squeeze the sponge out in used tank water to keep the beneficial bugs. do you find the sponge really dirty every time you clean it out?
to be honest, i think you should consider getting a bigger tank, splitting the fish into more than one tank or trying to find a pond as a last resort. that size tank if it is 12 gallons is only room enough for life for a fancy goldfish. This is only my opinion of course and what you choose to do is entirely up to you, please dont feel i'm trying to tell you what to do, i'm just offering advice. good luck and keep us posted on what you decide to do.