What’s wrong with this baby? Help please!

Just bought this baby a few days ago alongside another baby with my sister. Today I went outside and saw mine looking rough. I’m not sure if hers is bullying mine, and I don’t know what to do. I seperated them for now and brought him inside. The first day he was active, but mostly went under the other baby or nuzzled where my leg was. The second day I noticed he fell asleep a lot, and he also had watery poop. They had been acting like usual until today, which I got very worried because I see his beak messed up and his eye too. I brought him inside and because he’ll fall asleep very very often— I had to try my best to wake him up and try to get him to eat. I feel so bad for this baby, it’s only been 6 days or so.
I’m just confused if it has been like this since he hatched or I did something wrong? He was very sleepy when I got him but it seems like it got worse. I’m scared to put a heat lamp atm in case he is dehydrated because it is very hot.