Most likely no. I wouldn't be doing any private work at your age, I'm not sure if many places would accept you (if you're under a company, usually a matching serbice) or how liability insurance would work. For private work, there's always a risk of being trapped in a home or something happening to you. With how young you are I just simply wouldn't risk it until you're older.
For example, a few days ago I got choked out by a resident. But I yelled out and I had other CNAs nearby to help. I'm a grown man and this was an old lady. The risk is low and I'm sure companies have some vetting process but I just would hold off until you're 19 maybe.
Hospitals are more practical, they're more clean, they're more efficient, but they're a lot of patients. Usually you'd have a specialized role at that day in a hospital, e.g. being dedicated to solely readjusting people that day and someone else would do changing. But I don't know if all hospitals are like that, and you'd be doing floors of individuals.
The nursing homes I did my clinicals at were horrible - but it was because of the staff mainly not the labor. In nursing homes they have the lifts and shit and normally if a resident is too combative they'll relocate them, but I work in assisted living. Because we're not a nursing home, it means every transfer is manual- with my back and all.
I've actually really enjoyed working at an assisted living facility but, I think objectively the hospital would probably be the best option for you. What a lot of people in my cohort did was work as a sitter in the hospitals while they got certified so they could learn a lot at the hospital while learning the skills at school. Not a bad idea.