I agree...with that stock you should be doing more than a water change every couple of months. Weekly may seem like a lot, but it's actually very normal for tanks with less "messy" fish than yours. I'd also make sure you aren't completely throwing out all of the filter media. It shouldn't need to be replaced unless it is practically falling apart, but you can swish it around in tank water to get the gunk out. I don't use carbon, but it is different because it does lose its effectiveness with time. However, you should hopefully have some sort of sponge or floss as well and that is where a good portion of the beneficial bacteria are located, so by removing that you are essentially causing your tank to go through a smaller version of the cycling process (aka a "mini cycle").
On the topic of cycling, you should definitely give this a read:
Freshwater cycling
The nitrogen cycle quite possibly the most important process going on in our tanks. My guess is that your tank is at least somewhat cycled given its age, but without knowing your ammonia, nitrite, and nitrate readings it is only a speculation. I would highly suggest getting a liquid test kit (API's Master Kit, for example) and posting the results ASAP.
While I'm not very good at diagnosis....stringy, white excrement could indicate an internal parasite. Bloat itself is a symptom, not a disease, so it's very possible that something is infecting the fish. I think the first step would be to make sure the water quality is in tip-top shape.