Sadly, fish shops (and petsathome are really bad for this) routinely give out bad advice to new owners.
Cycling means ages of testing the water for the bad stuff (ammonia, then later nitrites and even then keeping a routine eye on the levels) while the bacteria build in the filter to sufficient levels to keep breaking down the amount of ammonia that the fish produce in their waste - and goldfish are very messy in the amount of waste they produce.
The 'leave water a few days' is poor advice. If you've done that then you are stuck with it due to rubbish advice, but will have to do very frequent water changes to keep the stress low for the fish. If you have a kind friend with a setup you can beg to have or borrow some of the sponge etc out of their filter to put in yours to speed up the cycling.
If you see them gasping at the surface they could be suffering from ammonia poisoning (the first threat as the levels build in the tank) and you need to do a water change.
Even when ammonia is under control, your fish can gasp at the surface (they look like they are cruising for food constantly). This can mean they are suffering from nitrote posoning. It's like humans with carbon monoxide. No matter how much oxygen in the water, they can't absorb it because the nitrite is preventing them. Again, the answer is swift, big and frequent water changes.
If you can get it cycled then they will quickly outgrow their tank I'm afraid. There is some truth in the theory that too small a tank stunts their outward growth. However, their internal organs grow normally and this damages their health.
Keep an eye out on ebay or freecycle for as large a tank as you can fit in and afford. I have 4 fancy goldfish in a 320L tank, 4 foot wide. It's lovely, and far easier to keep the fish in it healthy than it was in my 120L tank that DH first bought me.
Happy fish keeping.