Hi there fish help

Unfortunately without a filter, this will be an ongoing problem - unless you change about 70% of the water daily. If you were to get a filter (ie. a hang on back type that houses both sponge and ceramic) then it will cycle which means good nitrifying bacteria will grow on the filter media. This bacteria is fed by ammonia and once the filter is cycled, it will convert ammonia to nitrites to nitrates and nitrates are much less harmful than ammonia and nitrites.
Cycling a filter can take up to about 6-8 weeks and during this time, the ammonia and nitrites will climb to dangerous levels (which are reduced by daily waterchanges) and when you see nitrates appear, it will mean the cycle is kicking along smoothly

The problem without a filter is every hour of every day, fish excrete ammonia both via their waste and gills (which is kinda like pee) and the level of ammonia has nowhere to go but up and this is when you see the black smudges on the body. It's ammonia burn that's healing but unless the ammonia problem is fixed, the blackness will worsen and unfortunately your fish may die. They can withstand it for a little while but it stresses them badly lowering their immunity and once this happens, bacteria and illness can set in.
So if you can, try to grab a good filter ie. one that filters about 100 gallons per hour and in the meantime, I would up the waterchanges to daily until the skin heals. This will help your fish enormously