99% of the time any problems with these frogs is due to water quality. Removing the filter is a bad idea I would replace it immediately and put the old media inside of it to get your beneficial bacteria back.. I would also do a massive water change ASAP and I would recommend Prime as a water conditioner (don't use straight from tap).
Get an API liquid test kit.. what are your water readings? Ammonia/Nitrite/Nitrate?
I've never seen black/purple algae but it sounds really bad to me.. my guess is there was excessive shedding and skin irritation from poor water quality as they do use their claws to shed their skin.. but that's just my best guess.
I would worry more about getting the water quality under control than medication but maybe someone will chime in with medication ideas if necessary I've never had any experience with using meds for these frogs. If you get the water quality under control these frogs usually will recover.
Again I cannot stress enough for you and everyone else having problems with xenopus.. if your frog is sick or becomes injured or is acting odd or whatever 9 times out of 10 it's because your water parameters are off.
0 Ammonia (toxic)
0 Nitrite (toxic)
>20ppm Nitrate .. live plants can keep this under control.
Temp 68F to 72F too cold will compromise their immune systems too hot will cause stress and possible stroke 86F+ is lethal.
Heaters can burn these frogs, in most cases a heater isn't necessary if you can keep the water 68-72F which is room temperature.
Filters are necessary, these frogs create a lot of waste. The more filtration the better.. a good canister is ideal for HOB filters I like Tetra Whisper Internal filters.. over filter over filter over filter.. you can't have enough filtration. My 40G Breeder has 4 filters on it!
Water changes are necessary, change 25% of the water every week no matter how good your filtration is.
Condition your tap water.. chlorine is bad (toxic to frogs + kills your beneficial bacteria).. use something like Prime (I like prime because it neutralizes ammonia, nitrite, and various other toxic elements).
AqAdvisor - Intelligent Freshwater Tropical Fish Aquarium Stocking Calculator and Aquarium Tank/Filter Advisor is a good site to help you understand how much filtration you need and how much of a water change you need to do weekly.