I agree, they have Ascites. 
You have fed them layer feed for how long?  Options would be to feed an all flock/flock raiser type feed and provide oyster shell free choice for the laying hens.  Chick starter or grower can also be fed.
Layer feed had too much calcium for young growing birds.
You mention that you thought they had a parasite in their throat, or worms, or something...were they showing respiratory distress?  The fluid in the abdomen can cause those symptoms.
This is the ER forums, so quite normal LOL