Test strips are pretty unreliable. I would recommend saving up or getting your parents to purchase you a couple of API liquid test kits. That way you can see what's going on a bit more accurately.
You can break up a 50% water change into two 25% water changes, if you are concerned about harming your fish. Just leave a couple of hours in between and then do the second one. This way it won't be so much of a shock to go from a high level of nitrates to a low level all of a sudden.
Your goldfish tank is probably going to need 2-3 40-50% water changes a week if it's not an appropriate size. Because they produce so much ammonia, this gets converted to nitrate by your biological filter, which in turn builds up to higher levels in a small tank with infrequent water changes.
Seachem Prime is a really good water conditioner. It detoxifies ammonia, nitri
te and nitra
te, and is much more concentrated than a lot of brands on the market. I would highly recommend this if you don't already use it, as it can give you some breathing space between water changes.