It used to be like that in Brazil, but in recent years Anvisa (the Brazilian equivalent of the FDA) tightened policy on this and now people can only buy antibiotics with a prescription.
BTW, in my experience Brazilian doctors prescribe antibiotics a lot less than American doctors.
That's bad, but at least it's a two week course. Often people in India will buy a few days because that's all they can afford.
So this is the way it works in India. Most people who know a little english remember the brand name of the drug.
Others just walk to the pharmacy store and narrate the symptoms to the pharmacist. Typically: Sore throat, a little fever etc. Then they state their budget(10-20 rupees), the pharmacist gives two tablets of Azithromycin.
Even the EU is bad - Spain and Portugal allow OTC antibiotics (along with many Asian countries)
Can confirm South America.
Edit: a word