If I see a poor or needy person in the street and I want to give them zakah , should I try to find out if they are Muslims? is it different if the hospital is only treating children

Generally speaking, it is permissible to give zakat toward medical treatment of the poor. Children and adults stand on equal footing in this regard. Zakat payer must make sure that his zakat goes to its eligible recipients, this is unlike charity (sadaqa) which is permissible to give out for everyone alike.