Yes, when the beneficiary is genuinely poor or needy, zakat may cover his medical treatment or his fees, because Allah made zakat "for the poor and the needy" and the Prophet ﷺ described it as taken from the rich among them and given back to their poor. The sound approach is that a specific eligible person receives the benefit — you give him the money, or pay the hospital or school directly on his behalf with his knowledge — so that ownership of the benefit passes to him. What zakat is not for is general funding of a hospital's buildings, equipment or staff salaries, or a school's running costs, where no identified eligible recipient owns the benefit; that is a matter for voluntary ṣadaqah instead.
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.