Cory problem

Can you post your parameters, water test results and maintenance schedule?
Swimming in a spiral (and developing fin rot as a result of stress, for that matter) can be a result of poisoning, often from high ammonia or nitrite levels in the tank. Sick fish often refuse to eat, which _could_ account for the sunken stomach. Your cory isn't long for this world, it would be kind to euthanise him/her at this point.

Corys are quite sensitive to chemicals - medications, salt, and quite possibly algicides too
I've never used an algicide (otocinclus are better than anything that comes in a bottle for eliminating algae, IMO) so I can't tell you for sure but it sounds like this could be the cause of your problem. The fin rot could be a complication, brought on by stress.
I would do a 50% water change and add carbon to the filter. If there is something in the water poisoning them, whether it's the NO2 or another chemical, this will help to bring the levels down.
Continue to do daily water changes until your NO2 level is 0, and keep a close eye on your fish.
If you're having a major algae problem, many people on AC suggest blacking out the tank for a couple days. This won't harm live plants, but it will really put the brakes on algae growth. The water changes will also help eliminate the waste products like NO3 and PO4 that algae thrives on.
Keep us posted, good luck.

Cories are generally not good with poor water quality. But the first sign is usually the loss of their barbs. If these are gone then it quickly follows that they die off if conditions are not made better. It does sound like this fellow should be put down.

I would follow the advice of doing a rather large water change. And make sure to do 30-50% water changes every week to keep those cories healthy.

I had some cories doing the same thing and they eventually died but two others in the tank survived. I had a banjo cat in that tank and shortly after than moved him to another tank with some different cories. all of a sudden I had 1 dead and 2 other with ragged fins. I think I have attributed this to attacks from the banjo in the night. don't rule out the possibility of nocturnal predators beating the !@#$# out of them when you're not looking, especially from the ragged fins. what other tankmates do you have in what size of tank? Kyle