Your choice (distillation) is

But before doing distillation, we have to remove inorganic impurities and water.

You have shaken the organic solution with aqueous solutions of inorganic acid or base. That allowed small amounts of inorganic acid/base and water to stay in the organic layer.

First, let's wash* the organic solution to remove inorganic impurities.

Which liquid will you use?

Organic Web Chem University of Alberta