Doctors in Argentina are well trained and generally good. Many of them have their own practices as well as work out of hospitals, and frequently if they only work out of their own practices they will tend to make house calls, as long as you are within the same barrio. However, most private hospitals and insurers also have house-call hotlines that their members can access; Medicus is one insurer with a good reputation for ease-of-access for English-speaking patients.
Public hospitals, although underfunded, are typically good and have reliable care, however supplies and space are quite limited, so it is recommended to only use them only for emergencies. Private hospitals and practices offer excellent medical care and reasonable rates, even without insurance. Most staff at private facilities and hospitals will speak English.