When I bought my 4 barred rocks at the feed store, it was the same thing. The heat lamps were too far away, and they were the smallest in the bin, so I thought they were banties. Half of them had crusty butt which I ended up removing it and the down it was stuck to with nail trimming scissors (really sharp) Man it stunk! One of them limped for a good two weeks, and I kept on making sure it got to the water several times a day. Now they are all doing great! I felt even if they died, at least they'd have a warm, comfortable place for a while, with a little bit of love. I can't blame you one bit! They have actually turned out to be my favorite. They are quiet, gentle, and like to be held. Except the roo in the quartet-- I think he's still mad at me for the whole crusty butt surgery thing. But even he is gentle, just avoids being picked up.
I feel so sorry for all these chicks who don't get bought and who knows what happens to them? I've been avoiding the feed store, since I already have 16 (10 are from the feed store-meaning accidental purchases). Now I know next time I need chicks I can get them from the feed store and not worry about shipping. But that will be a few years at this rate!
Anyway, I hope your little one makes it!