Help, I think my duckling is sick!?

I got two ducklings about a week ago, one was a few days old, the other was about a week. I let the ducklings swim in a sink for awhile, my boyfriend watched them as I was cleaning their Cage. When I came back I noticed the older one has a red mark on his neck and his down is missing some. I looked closer and some more down is missing on his back and his skin there is also red, I know after awhile they lose some down to grow feathers and start to look like a duck. But when I took him out dried him some and put him in the tank, he kept on falling, while the younger one was waddling back and forth to his food and water. I put my snake heat lamp over the tank to heat it up some just in case they were cold (they werent completely dry, and I keep them in my room that gets a little chilly) But the (sick?) one walked to the other side and layed under the lamp. Im really worried and cant find anything online. Please help!