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My mom's taking care of an RES my cousin just got. He's as small as a Quarter.
He barely moves, he looks miserable. My mom fed him shrimp she got at Petsmart and he finaly started moving a little. His tank is ok for his size now and it has a filter but not a good light.
Today we got home (I'm visiting my mom this weekend) and he looked dead. He wouldn't move at all. He's just so scared.
Can you tell if they're sick?
I think I should take him home with me. I wouldn't put him in the same tank as Greeny of course because he might be sick.
Greeny used to be just like him but now she's a little trouble maker. Whoever said turtle's don't have feelings lol. I say Greeny's name and she swims towards me and pops her head out of the water. She loves running around and she actually comes when I start making funny voices.
Maybe If I take care of the little guy he'll get better... What should I do?

what does he look like?
are his eyes closed? possibly swollen or a little bit puffy?

no not puffy at all. he looks normal like Greeny did. He's on the right.

maybe he is just shy? and i think taking him home iwth you would just stress him out and possibly cause him to get sick. maybe just leave him where he is so he can get used to it and comfortable with it and the people who surround him

the thing is that i have the right setup and the lighting he needs.

then bring it to where he is.
because if he is sick you dont want to put him in the set up greeny is in, as you already said.
but if you think its like animal abuse or something then you should take him to your house, but from what it sounds like it just seems like a few begginer issues.

Without the right setup, a hatchling won't have a good chance for survival. Water temps, basking area and diet are what you really need to get setup right away then work on the filtration, UV should be next.

Remember, many hatchlings are scared and shy, don't handle them too much and give them some privacy.