Lungfish looks sick!

Dear friends,

My lungfish is about 10". 2-3 weeks ago I started noticing thin, whispy, membranous skin shedding which is quite generalized (whole body). It's fins used to be long and slender. Lately they have lost its sharp ends, and they appear considerably shorter now and have blunt ends. It's more lethargic, but still feeds as normal. My water quality hasn't changed for the 1 year I've had it. There's no filter but I do a full water change once in 3 days. I feed it sinking pellets and occasionally earthworms.

Any oe has any idea what's wrong? Thanks!

Dear friends, thanks to all your replies. Will get on it right away!

Hey guys.. okay updates! My lungfish is doing well now. I've installed a canister filter, with seeded media from my other tank.
The shedding has stopped since about 2 weeks ago. It's no longer lethargic and feeding is back to normal. However the fins have blunted quite a bit. They will probably take some time to grow back. Thanks for the prompt replies from earlier!

Hey guys, another question. Its fins are back (they grow amazingly quickly) and colour's back to normal. However there's something I noticed which troubles me a little. It hasn't pooped in 3-4 weeks. Appetite is great, usual carnivore pellets, plant algae pellets. Stomach doesn't look bloated at all. BUT no poop for 3-4 weeks? That's a little worrying.

Any idea anyone?