Panda cory with velvety skin?

Hi all,
I bought three neons and a couple of panda cories from a LFS (that has good yelp reviews and ratings). Two neons died on that day and panda cories have red swollen gills. Besides that, their skin seems like covered by white velvety stuff. As soon as I noticed that, I moved them to my QT tank and have been watching them since yesterday. They look morbid and spend most of the time at the bottom just sitting, but they do eat okay. I am not sure what I need to do at this point. I never lost any of my other neons and cories from Petsmart and they are still doing great, so I suspect that the LFS wasn't that great place as yelp said.
My question is will frequent water change (daily ~50%) save these guys eventually or do I need to either medicate or euthanize them? I'd really appreciate your advice.

I will try to post some pics later tonight. I didn't use QT before, since I only had a tiny 6 gallon, but I upgraded to a 10gallon a week ago, so now my empty 6g became my QT. I didn't QT them when I bought them from the LFS - I guess I trusted them too much. My water params all zero, (checked once or twice everyday since upgrade and did 50% biweekly water change) and temp has been slightly high (~80oC) since heat wave around north cal, but all other fish in my tank are doing okay as usual.

Pic of my sick cory

They look still the same, not moving, but still eating. There fins also look more shredded or torn and whitish around the edge. Tank temp has been definitely high for several days, since it was almost 100 during the weekend. It's too bad that they are so sensitive. I'm leaning toward euthanizing them. I guess my tank is not ready for these guys yet.

My pandas are still alive!

I just want to give an update to those of you who gave me advice.

So after I moved them into my QT tank, I kept doing 80-90% WC every day and feed them once a day. They seemed inactive and mostly sat at the bottom, so at first I didn't think they were eating, but I put flakes before I was off to work and after I came back home, the bottom was always clean so I figured they did eat. When I did WC, I added some ammo-lock and aquarium salt but any medication (didn't have one). After a couple of days they started swimming around and their velvet coating also started disappearing overtime. One of them was completely recovered and the other (the guy in the previous picture) had very severe tail fin rot but seemed to regrow again, so I moved both of them 3 days ago to the main tank and they are doing great so far. I am very proud of myself and my cories now.