I would say that daily water changes as close to 100% are required. Please do your best to get a new home for this guy, at least five gallons. Clean, warm water is always beneficial. He needs his water to be around 80 degrees.
It is very difficult to unreliably cycle a tank under five gallons. It's difficult to maintain water quality in the smaller tanks because you have less volume for dilution so ammonia, nitrite, and nitrate build up rather quickly.
Something like that looks extremely painful. I would start taking care of this by improving water quality and getting some antibiotics on hand, just in case. If this is an open wound, your fish may get an infection which would kill him if this tumor thing doesn't.
Hope he gets better soon. Looks awful.