So you think being a republic means you're NOT a democracy???
A true democracy is in essence a structure that in all circumstances the will of the majority of all the people determines how the government will be directed. A Republic is a system whereby people in designated areas select someone to represent them and give full authority to that individual.
Different States have given certain structured guidelines as to the way a selected individuals is to cast a ballot. The selected individual however may not be required to cast a ballot the way the popular vote results made If the state gave them full discretion to cast their vote. This is how the Presidential or National election system Is done.
Congress is made up of individuals who were elected by a specific area of the country and is elected and represented by the popular vote of that area.The Representatives presumably are expressing the preferences of the area they were elected to. The senate however has only 2 individuals per state who are supposed to represent the party they ran for in the election at the state level.
Democracies are totally driven by majority of people and Republics are a structure to allow Elected individuals to represent the ideology of a group or political party.
The USA is a republic structure by design and is utilized to place people in certain positions to carry out the presumed will of the people they are elected from.