Sorry if I came off rude. It was late and I was just about to go to bed.
I agree with what Calmwaters said about removing the carbon. It's relatively easy just to make a slit in the filter cartridge and shake out the carbon. I honestly don't use carbon in any of my tanks anymore. I find it useless and it just gets in the way. So, I make my own filter media now out of blue filter sponge. Just cut a piece off the big rolls that come in a bag and stuff it in the filter. Ta-da.
Doing only 10-15% water changes twice a week is not going to keep your ammonia and nitrite levels as low as possible, even with just the betta in there. Daily 50% water changes are the only thing that are going to help. At this point, I'd honestly recommend going out and getting a bottle of Tetra Safe Start (TSS). Restart your tank completely (basically do a 100% water change), add the TSS, and wait for ten days. Your tank will be cycled then because TSS contains the necessary beneficial bacteria to jump start your cycle, in suspended animation. Don't be fooled by other products like NutraFin Cycle and the like. They are composed of land-based bacteria that will create a false cycle and after they die (usually within a week or so), you're back to square one.
Calmwaters is also absolutely correct about what will happen to your pleco if kept in a tank too small for it. It doesn't matter if you upgrade to a 10gal, even as soon as possible. The tank is still too small for it and it will die a very painful death if not kept in a properly-sized tank and allowed to grow like normal.
I'm sorry if none of this is what you want to hear. I am a moderator on a couple of fish forums (one betta forum and a friend's general fishkeeping forum) and I have learned a valuable lesson: I have had to become more concerned about the welfare of your fish than I am about your feelings. I would suggest going to a tropical fish forum called FishLore.com (Fish Lore's Aquarium Fish Forum
). There are great, knowledgeable people there who will help you tremendously. Another site I'd recommend is the betta forum I'm a mod on. It's called Betta Fish Forums. Here's the link: Betta Fish Forums
I know you said you are a zoo keeping technology major and that you have an emphasis in tropical fish keeping, but I would suggest forgetting everything you think you know and starting back at square one with the forums I suggested (especially FishLore...it's a great community...a lot like here, actually). Trust me, I had to do the same thing. Pretty much every fishkeeper does. I don't know anyone who comes into the game knowing everything. And whoever told you that you could put a pleco in a 5.5gal and upgrade the tank when he gets a bit bigger...stop listening to that person. They're going to get your fish killed.