Morning. I am currently in the process of drinking a lot of coffee so I hope this makes sense 
Yeah, the shop has cocked up here and given you some shocking advice. Don't feel bad, this happens to pretty much everyone when they start out with fish. It's infuriating but really it is completely reasonable to expect someone who is selling something to at least know a bit about it. But anyway.
Yes, you need to carry on doing as many water changes as possible in the next few weeks. The tank isn't cycled so you need to keep the ammonia and nitrIte down. You will also need a water test kit like this one (this is a good brand so I'd go for this one, but you might save a couple of quid if you shop around). Monitoring the water is a very important part of fishkeeping, it is not just for the experts. You have complete control over their environment so you need to know what's going on.
Adding less tap safe is bonkers
never listen to the shop again! There are a lot of bacteria products that are meant to instantly cycle a tank, but I have never tried one that actually works. I wouldn't bother with them, good old-fashioned water changes are what you need. You could use Ammolock which converts the ammonia into ammonium, which is less harmful, but still allows the tank to cycle. I wouldn't worry about buying stuff to reduce nitrAte unless your tap water nitrAte is really high (you'll need to test it). Not sure what there is to reduce nitrItes but this can all be done with water changes so I'd probably just stick with that.
What sort of filter do you have and what sort of sponges are in it? A lot of filters these days are crammed full of chemical filtration (which really fucks me off) and that will make a big difference to the cycle. It is very important to never wash the filter in tap water because the chlorine in it will kill the good bacteria.
You didn't mention how big the tank is. This may be a problem for you, but goldfish do grow very, very big- it is a myth that they grow to the size of their tank.
I'd be tempted to find a different shop too. Tbh, the majority of places that sell fish are pretty crap, but you do get the odd one that employs total geeks that know what they're doing. And you are more likely to get healthy stock in those places because the staff know how to treat ill fish and monitor water quality.
After I've had more coffee, I'll probably think of something else. But I hope that helps for now.