No, we ARE a Democracy. Our form of Democracy is a representative republic with checks and balances (such as the Senate) so that we do NOT HAVE a direct democracy. History has proven that direct democracies will eventually lead to totalitarianism. Democracies come in many forms and I am grateful for the one we have and are trying to preserve.
We are a Federal Republic regardless of how our Representation is elected.
We became closer to a “pure” Democracy when they stupidly allowed the direct election of Senators.