Hi
My bet would be pasty butt.
The vent (anus) becomes caked with dried faeces and the chick can't eliminate waste. The cheeping is usually as it strains to do so and as food backs up in the system it becomes pretty desperate and constant.
If it looks like I'm right, get half a cup of warm water with a few crystals of epsom salts if you have them and sit the chick in it to soak. Gently rub/massage it's vent to help loosen the caked on poop and supervise carefully whilst it is soaking in the water so that it doesn't drown. Don't soak for more than 15 mins at a time but you may need to do it several times the first day to get things fully cleaned out. Dry thoroughly with kitchen paper and or warm (not hot) hair dryer and smear a little petroleum jelly or olive oil on it's vent each time to prevent further caking. Make sure the chick drinks plenty (mixing chick crumb into a wet mush with water and a little olive oil may help) and that the brooder is not too hot and has a cooler side the chicks can move to if they are feeling too warm.
Good luck with it. Hopefully, I am right about the cause, as it is reasonable easily solved.
Regards
Barbara