If you are trying to use medications in your tank, you need to remove the carbon filter completely and keep it out until you are done with your treatments. This might be why it is turning brown. In general, your success with an aquarium does not hinge very strongly on carbon filtration and in fact, I don't use it any longer in any of my tanks unless I need it to remove medications (which I hardly ever use) or clear up the water after putting driftwood or something like that in the tank. It is basically just there to soak up things that might discolor your water and to help with odors...both of which you should have no problem avoiding in the first place.
When you are replacing your filter media, it is important to know that a lot of your beneficial bacteria is living within it. If you are just changing the carbon, then you should be ok....but because of your stocking and current problems, I would do my very best to protect and keep the other types of filter media your filter contains. True, the bacteria is also lining in/on your substrate, decor, etc...but it does best when the water, and hence the ammonia and nitrites, are brought directly to the bacteria instead of the bacteria swimming around in the water to search for food. So, that said, obviously your filter is simply a place for bacteria to grow and it supports that by bringing water through the media.
I agree whole-heartedly with BMueller in that your tank is severely overstocked. As was pointed out, even if all the fish you have are very tiny, there is just too many fish in the tank and your beneficial bacteria are probably having a very hard time removing all the wastes that are being created. I would feel confident to place a bet that your tank either has some ammonia or nitrite levels right now (when you want them to both be at 0 ppm or close to it) or has a very high nitrate level. Nitrate is still toxic to your fish, only in higher quantities than ammonia and nitrites. Personally, I would do a water change before my nitrate levels reach 50 ppm. If any of the 'big three'...ammonia, nitrites, nitrates....are present in your tank at higher than ideal levels, they do create stress for your fish.
And stress leads to a huge array of potential problems for your fish such as every issue you are experiencing right now. IME, both fin rot and Ich takes weeks, if not a month or more to 'cure' so be patient. Obviously, it is hard to judge the progress of treating fin rot because first you need to cure it, and then you need to allow time for the fins to grow back. To be really honest, I feel that your fin rot issue is not really fin rot, but rather fin nipping from other fish which has been exacerbated by the over stocking in your tank. Even though all your fish are community fish, which implies that they are all nice and peaceful, overstocking can easily change that behavior. It is good to use an antibiotic anyways though since open sores often lead to infections. As far as Ich goes, if you have one or two fish with white spots on it, you will soon have others. It is very contagious and since your fish are all pretty stressed, they are not 100% able to fight Ich off. No matter what, make sure that you continue to treat for Ich AT LEAST two weeks after you notice the last white spot has dissapeared from all your fish. If you dont, you are very open to a reoccurance of Ich which is never a good thing obviously.
If this was my tank, the first thing I would do would be to address the overstocking issue somehow. I would definitely take the Bala Sharks back to the LFS since they get too large for even a 55 gallon tank. Check out this photo of some mature bala sharks that were at the Shedd Aquarium, which I visited recently:
...and yes, that is my hand and no, I am not a midget
After that, I would choose to keep either the gouramis or angels and remove all of the others. (e.g. if you want the angels, take the gouramis to the LFS). Both are known to be semi-aggressive and both get relatively large for your tank size. You may also run into some issues with adult gouramis or angels being able to fit smaller fish like neons into their mouth. It is ALWAYS a good idea to consider mouth sizes since very few fish will pass up a tankmate as a snack, even if they are herbavores.
From there, I would probably choose between the bleeding hearts or neons, similarly to angels versus gouramis. I believe that both fish are better off in a school/schoal, so you are good there, so as a bare minimum, I would cut your current schools/schoals in half of what they are right now.
I know this is hard information and ideas to deal with and trust me, we are not picking on you. I am sure most of us overstocked our aquariums at one time or another, which led to problems like the type you have right now and so we learned the hard way. I would almost promise you that by reducing the number of fish in your tank, you would see an instant improvement in your fish....maybe not as far as fins growing back overnight or the Ich jumping out of the tank, but you will certainly notice that these issues slow down or fail to progress any more.
Whats Wrong With My Tank?! 
