Sorry for taking a long time to reply. He is an only turtle, I had another one but it died in Febuary. The other turtle which was bigger than he was used to snap at him when I first got them into the tank. But later they got along and ignored each other. I once tried to feed him vegetables and he took interest in carrots, he never ate any vegetables while being with me for almost 3 and a half months. He took a nibble and the tiny bits of carrots I put there but I don't know if he swallowed it. He eats mostly 3-6 pellets a day, depending on which one I feed him. The two kinds of pellets I feed him are HBH Turtle Bites, they're multicolored and round. The other kind are Nutrafin Floating Turtle Pellets, which are long and brown. I also occasionlly feed him some ReptoTreat brand shrimp. There's no gravel in the tank. Sometimes while swimming I'll see him blow out a bubble or something. I don't know if he poops regularly but when I take out the thermomiter that stays in the water it's pretty slimey. In the last two days he's been doing well and not worrying me as he usually does. He's been really active. Yesterday he basked for a long time until I shut off the lamp. Today when I came home he wasn't in his usual spot he was under the ramp and inbetween the gap of it and the Rubbermaid. I've seen him diving looking for food down under which he hasn't done yet. The only thing that puzzles me about him is after I lift the cover off the Rubbermaid (It's only half on I use it so nothing falls inside.) and he's on the ramp on the dry side sleeping. Maybe if there's noise during the night before I wake up that he hears he goes to his regular place and sleeps there.
Also I was wondering can I just use my UVB bulb to give off heat since the UVB also gives out UVA. When moving it around it gave off the proper basking temp. and he basked. And about the mucus around the nose and swollen eyes I really don't know because I don't know if it looks different on a turtle. Here's a picture:
Also here's a picture of my bulb to verify that it's the proper kind:

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