@Lolzlil,
I had and still have the exact same thing on my goldfish.
The urine in the water, burns their gills.
The pet store advised me to change only half the water, once a fortnight and fully change it the following fortnight. He said you can't over do chlorine neutraliser, but suggested around 5 drops for a small fish bowl. Also, he advised and so I purchased, live plants as they breathe oxygen.
The burnt mark is still on my goldfish but it hasn't got worse and that was 3 months ago.
I follow the above.
Filters are your better bet but the above is ok as well.