It sounds like pasty butt and you need to soak the chicks bottom in a cup of warm water and gently rub it's vent to release all the caked poop. It will be swollen because it is clogged up and only a small amount of urates can pass and these crust up even more. Regular bathing and then I would apply an antiseptic ointment if the chick has been pecked. It will die if you don't get in unblocked, so don't delay. You can understand it not wanting to drink if it cannot poop. A moist cotton bud (q-tip) is a useful tool for gently easing the caked poop off it's vent after you have soaked it. Be careful to supervise the chick whilst it is soaking so that it doesn't drown. Soak for a good 10-15 mins each time.
Usually pasty butt is a symptom of the brooder being too hot.... you may want to check that and perhaps reduce the temperature or create a cooler part in the brooder where the food and water are.
Good luck
Barbara