Is public International Law a type of law?

Of course it is. Public international law are rules that concern relations between Government(al organization)s and civilians, with an international dimension. The rules can be developed in multilateral treaties and as you know, a treaty is a form of law. Therefore public international law is law. Even unwritten laws such as customary law of countries or cultures are perceived as legitimate laws.

AnswerInternational Law is not law in the same way as domestic law is law. Countries that allow international law to be broken by their citizens in their borders are free to prosecute or ignore at their discretion.