Has there ever been an independent senator or house representative?

Sure. Bernie for example.

Yes, although the Independents caucus with one party or the other.

As @stanleybmanly mentions, Bernie Sanders is a political independent, as was his predecessor Jim Jeffords. Angus King of Maine is also independent. All three Senators caucus(ed) as Democrats.

According to Wiki…

The United States House of Representatives has also seen a handful of independent members. Examples include Bernie Sanders of Vermont, Virgil Goode of Virginia, Frazier Reams of Ohio, and Victor Berger of Wisconsin. In 2012 Angus King was elected to the US Senate as an Independent from Maine. As of 2016, he has typically caucused with the Democrats.

It happens more frequently that the 2 major paties prefer to admit!!!

Joe Lieberman I don’t think was mentioned yet.

There has to be others.

Most independents I think previously were with the Republicans or the Democrats and changed, some go back.