The ick and rot were due to water quality issues from not changing the water enough and severe overstocking
There is no point in filtering a bowl of that size. It will only cause stress. You also need to be doing daily 100% changes in something this small, or at least 50% 100% alternating... how are you keeping it warm? That's the most important thing..
Actually the most effective treatment for ick is simply clean water and heat.. 86-88F for at least 2 weeks and one week past the last sign of ick. Fish must be acclimated to this very slowly at no more than one degree per hour and 5 degrees per day to avoid stress and/or shock. You can add aquarium salt at 1 tsp per gallon predissolved but you don't need to.
The smallest of corys require 10g.. some require much larger. What species do you have? Neon tetras require a 10g and should be kept in schools of no less than 5. You need to upgrade your tank or rehome the other fish.
Your 6.6g tank is not cycled if you have ammonia. What are your nitrite and nitrate readings? You needed to be doing weekly 50% water changes with siphon in something of that size, once it is fully cycled. Cycling can take up to two months and during that time a daily test for ammonia and nitrite and do a 50% change any time you see either. First ammonia will spike, then nitrite. Ammonia will stick to 0 first, then nitrite leaving you with only nitrates. The weekly change described above should keep them <20ppm. http://www.bettafish.com/showthread.php?t=47838
Your readings are suggesting it has barely even begun to cycle.
Here's how to do large water changes in your QT without shocking:
In the 50% I would suck through the gravel with a turkey baster to remove poop and half the water. I would refill it with same temp water (use tank thermometer to match running tap water) that already had conditioner added to it. I use 1 gallon water jugs like you can buy at the grocery store - rinse thoroughly before using with hot water but not soap or chems).
For the 100% he'll need to be removed. I would cup in an opaque plastic solo type cup and wrap a towel for heat. Thoroughly rinse the tank, gravel and decor but don't use soap or chems. Refill with same temp water, add conditioner, stir it up a bit then float him in the bowl an hour while slowly adding a couple tablespoons of new water to his cup every 10 minutes. Finally release, keeping as much of the old water in the cup as possible. He shouldn't show any signs of shock this way.