Welcome to BYC
When chicks first hatch, they will roll around and scream as if they are dying in pain - but it's totally normal. If your chick is acting lethargic,
feels/looks swollen, isn't interested in either food or water, &/or has a swollen, unclosed and bloody umbilicus, I'd suspect mushy chick, which
is an infected yolk sac, basically. It is caused by bacteria somehow intering the egg during incubation, and there isn't really a 'treatment' for chicks
this young. Some will make it, some won't. Seperate this chick from the others, have food available, though he probably wont eat. Dip the tip of his
beak in the water every couple hours, and offer a heat source that he can move away from - if need be. If he doesn't make it, he should pass with-in
6-10 days or so. As for the bottom, clean it with a warm damp cloth. Hold it on there until whatever is stuck - loosens up in which you can wipe it off
with an ease. I am not by no means saying your chick HAS mushy chick disease, I am just stating the possibility, Remember that HEALTHY new born
chicks are likely not to eat for 2-3 days after hatching, due to the absorbed yolk sac, and to be tired and unable to walk correctly. Wait it out
Stuff
like this happens, in the world of chickens.
Wishing you luck